A fair dice is thrown twenty times. The probability that on the tenth throw the fourth six appears is -Maths 9th

1 Answer

Answer :

(c) \(rac{84 imes5^6}{6^{10}}\)In the first nine throws we should have three sixes and six non-sixes and a six in the tenth throw and thereafter whatever face appears, it doesn’t matter. ∴ Required probability = 9C3 \(\bigg(rac{1}{6}\bigg)^3\) x \(\bigg(rac{5}{6}\bigg)^3\) x \(rac{1}{6}\) x 1 x 1 x 1 ............x 1 {10 times} = \(rac{84 imes5^6}{6^{10}}\).

Related questions

Description : Two dice are thrown. Find the probability of getting an odd number on the first die and a multiple of 3 on the other. -Maths 9th

Last Answer : Let A : Getting an odd number on first die; B : Getting a multiple of 3 on second die, thenA = {1, 3, 5}, B = {3, 6} ∴ P(A) = \(rac{3}{6}=rac{1}{2}\), P(B) = \(rac{2}{6}=rac{1}{3}\) ... B are independent∴ Required probability = P (A) . P (B) = \(rac{1}{2}\) x \(rac{1}{3}\) = \(rac{1}{6}\)

Description : In a single throw of two dice, what is the probability of getting a sum of 9? -Maths 9th

Last Answer : Outcomes with sum of 9 = { (3, 6), (4, 5), (5, 4), (6, 3) } P ( getting a sum of 9 is ) = 4/36 = 1/9

Description : Two dice are thrown simultaneously 500 times. -Maths 9th

Last Answer : (i) P (getting a sum more than 10) = P (getting a sum of 11) + P (getting a sum of 12) = 28/500 + 15/500 = 28 + 15/500 = 43/500 = 0.869 = 0.09 (ii) P (getting a sum less than or equal to 5) = P ( ... + P (getting a sum of 10) + P (getting a sum of 11) = 53/500 + 46/500 + 28/500 = 127/500 = 0.254

Description : Two unbiased dice are rolled. Find the probability of getting a multiple of 2 on one die and a multiple of 3 on the other die ? -Maths 9th

Last Answer : When two unbiased dice are rolled, the possible out comes are∴ n(S) = 36 Let A : getting a multiple of 2 on one die and a multiple of 3 on the other die. ⇒ A = {(2, 3), (2, 6), (4, 3), (4, 6), (6, 3), (6, 6), (3, 2), ( ... (3, 6), (6, 2), (6, 4)} ⇒ n(A) = 11∴ P(A) = \(rac{n(A)}{n(S)} =rac{11}{36}.\)

Description : Three identical dice are rolled. The probability that same number will appear on each of them is -Maths 9th

Last Answer : (d) \(rac{1}{36}\)Total number of outcomes when three identical dice are rolled, n(S) = 6 6 6 = 216 Let A : Event of rolling same number or each dice ⇒ A = {(1, 1, 1), (2, 2, 2), (3, 3, 3), (4, 4, 4), (5, 5, 5), ... 6)} ⇒ n(A) = 6 ∴ P(A) = \(rac{n(A)}{n(S)}\) = \(rac{6}{216}\) = \(rac{1}{36}\).

Description : Two dice are rolled simultaneously. The probability of getting a multiple of 2 on one dice and a multiple of 3 on the other is -Maths 9th

Last Answer : (c) \(rac{11}{36}\)Total number of outcomes when two identical dice are rolled, n(S) = 6 6 = 36 Let A : Event of rolling a multiple of 2 on one die and a multiple of 3 on the other die ⇒ A = {(2, 3), (2, 6), (4, 3), (4, ... , 4), (3, 6)} ⇒ n(A) = 11 ∴ P(A) = \(rac{n(A)}{n(S)}\) = \(rac{11}{36}\).

Description : Two dice are rolled once. Find the probability of getting an even number on the first die, or a total of 7. -Maths 9th

Last Answer : (c) \(rac{7}{12}\)Total number of ways in which 2 dice are rolled = 6 6 = 36 ⇒ n(S) = 36 Let A : Event of rolling an even number of 1st dice B : Event of rolling a total of 7 ⇒ A = {(2, 1), (2, 2) , (2, 6), (4 ... (rac{18}{36}\) + \(rac{6}{36}\) - \(rac{3}{36}\) = \(rac{21}{36}\) = \(rac{7}{12}\).

Description : Two dice are thrown together. Find the probability that the sum of the numbers obtained is even a. 1/4 b. 1/6 c. 1/3 d. 1/2

Last Answer : d. 1/2

Description : A dice is thrown once, what is the probability of getting a prime number? a. 1/3 b. 6/25 c. 1/2 d. 1/4

Last Answer : c. 1/2

Description : Two dice are thrown together. The probability that the total score is a composite number is: A) 5/12 b) 12/7 c) 7/12 d) 12/5

Last Answer :  Answer: C)  Clearly, n(S) = (6 x 6) = 36. Let E = Event that the sum is a composite number Then E= { (1, 3), (1, 5), (2, 2), (2, 4), (2, 6), (3, 1), (3, 5), (3, 3), (3, 6), (4, 2), (4,4),(4, 5), (4, 6), ( ... 5,3),(5,4),(5,5),(6,2),(6,3),(6,4),(6,6) } n(E) = 21 P(E) = n(E)/n(S) = 21/36 = 7/12.

Description : When two dice are thrown, find the probability of getting a greater number on the first die than the one on the second, given that the sum should equal 9. A) 1/2 B) 1/5 C) 2/5 D) 4/2 

Last Answer : Answer: A) Let the event of getting a greater number on the first die be G. There are 4 ways to get a sum of 9 when two dice are rolled = {(3,6),(4,5),(5,4), (6,3)}. And there are two ways where the number on the ... Now, P(G) = P(G sum equals 9)/P(sum equals 9) = (2/36)/(4/36) = 2/4 =>1/2

Description : A die is thrown six times and number on it is noted as given below : -Maths 9th

Last Answer : Here, in 6 trials, each number occur once and total prime numbers i.e., 2, 3, 5 occur one time each Hence, the number of prime occur = 3 Probability of getting a prime = 3/6 =1/2

Description : A die is thrown six times and number on it is noted as given below : -Maths 9th

Last Answer : Here, in 6 trials, each number occur once and total prime numbers i.e., 2, 3, 5 occur one time each Hence, the number of prime occur = 3 Probability of getting a prime = 3/6 =1/2

Description : A die is thrown.What is the probability of getting a multiple of 3 on the upper face ? -Maths 9th

Last Answer : Multiple of 3 on a die = 3, 6 ∴ P (a multiple of 3) = 2/6 = 1/3.

Description : A die is thrown twice. What is the probability that at least one of the two throws comes up with the number 3 ? -Maths 9th

Last Answer : (b) \(rac{11}{36}\)Let S = total ways in which two dice can be rolled ⇒ n(S) = 6 6 = 36 Let A : Event of throwing 3 with 1st dice, B : Event of throwing 3 with 2nd dice. Then, A = {(3, 1), (3, 2), (3, 3), (3, 4), ... ) - P(A ∩ B)= \(rac{6}{36}\) + \(rac{6}{36}\) - \(rac{1}{36}\) = \(rac{11}{36}\).

Description : What is the probability if a fair dice rolled on 2?

Last Answer : Assuming a standard 6-sided die with sides numbered {1, 2, 3, 4,5, 6}, then:Number of successes = 1Total number of outcomes = 6→ pr(2) = 1/6

Description : Consider an experiment of tossing two fair dice, one black and one red. What is the probability that the number on the black die divides the number on red die ? (A) 22 / 36 (B) 12 / 36 (C) 14 / 36 (D) 6 / 36

Last Answer : (C) 14 / 36 

Description : A coin and six faced die, both unbiased are thrown simultaneously. -Maths 9th

Last Answer : (c) \(rac{1}{4}\)Let A : Event of getting a tail on the coin B : Event of getting an even number on the die. Then, P(A) = \(rac{1}{2}\)P(B) = \(rac{3}{6}\) = \(rac{1}{2}\) as B = {2,4,6}A and B being independent events ... die)= P(A ∩ B) = P(A) P(B) = \(rac{1}{2}\)x\(rac{1}{2}\) = \(rac{1}{4}\).

Description : In a throw of a die, find the probability of not getting 4 or 5. -Maths 9th

Last Answer : Required probability = 1 – P(4) – P(5) =1- 1 / 6 - 1 / 6 = 4 / 6 = 2 / 3

Description : In a throw of a die, find the probability of not getting 4 or 5. -Maths 9th

Last Answer : Required probability = 1 – P(4) – P(5) =1- 1 / 6 - 1 / 6 = 4 / 6 = 2 / 3

Description : In a throw of a die, find the probability of getting an even number. -Maths 9th

Last Answer : Total even number on a die = 3 P (getting an even numbers) = 3/6 = 1/2

Description : A dice is rolled number of times and its outcomes are recorded as below : -Maths 9th

Last Answer : Total number of outcomes = 250 Total number of outcomes of getting odd numbers = 35 + 50 + 53 = 138 P (getting an odd number) = 138 / 250 = 69 / 125

Description : A dice is rolled number of times and its outcomes are recorded as below : -Maths 9th

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Description : Three fair coins are tossed simultaneously. Find the probability of getting more heads than the number of tails. -Maths 9th

Last Answer : (d) \(rac{1}{2}\)Let S be the sample space. Then, S = {HHH, HHT, HTH, HTT, THH, THT,TTH, TTT} ⇒ n(S) = 8 Let A : Event of getting more heads than number of tails. Then, A = {HHH, HHT, HTH, THH} ⇒ n(A) = 4∴ P(A) = \(rac{n(A)}{n(S)}\) = \(rac{4}{8}\) = \(rac{1}{2}.\)

Description : A Police man fires six bullets on a decoit. The probability that the decoit will be killed by one bullet is 0.6. What is the probability that the -Maths 9th

Last Answer : Let Ai be the event that the decoit is killed by the ith bullet (1 ≤ i ≤ 6). Then \(\bar{A}_i\) is the event that the decoit is not killed, ∴ P (Ai) = 0.6 and P(\(\bar{A}_i\)) = 1 − 0.6 = 0.4∴ Probability ... decoit p = 0.6 ⇒ q = 1 − p = 1 − 0.6 = 0.4Required probability = qqqqqq = (q)6 = (0.4)6.

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Description : When a dice is thrown, the outcomes are ______.

Last Answer : When a dice is thrown, the outcomes are ______.

Description : In tossing a coin 100 times head appears 56 times. -Maths 9th

Last Answer : P (head) = 56/100 = 0.56.

Description : A coin is tossed 500 times and we get Heads : 285 and tails : 215 times. When a coin is tossed at random, what is the probability of getting a. head? b. tail? -Maths 9th

Last Answer : Given, Total number of events = 500 No. of times heads occur = 285 Probability of getting head when coin is tossed at random = 285/500 = 57/100 No. of times tails occur = 215 Probability of getting tails when coin is tossed at random = 215/500 = 43/100

Description : Two coin are tossed 400 times and we get a. Two Heads : 112 times b. One Head : 160 times c. No Head : 128 times. When two coins are tossed at random, what is the probability of getting a. Two Heads b. One Head c. No Head -Maths 9th

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Description : A coin is tossed 500 times and we get Heads : 285 and tails : 215 times. When a coin is tossed at random, what is the probability of getting a. head? b. tail? -Maths 9th

Last Answer : Given, Total number of events = 500 No. of times heads occur = 285 Probability of getting head when coin is tossed at random = 285/500 = 57/100 No. of times tails occur = 215 Probability of getting tails when coin is tossed at random = 215/500 = 43/100

Description : Two coin are tossed 400 times and we get a. Two Heads : 112 times b. One Head : 160 times c. No Head : 128 times. When two coins are tossed at random, what is the probability of getting a. Two Heads b. One Head c. No Head -Maths 9th

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Description : A die is rolled three times. The probability of getting a larger number than the previous number each time is: -Maths 9th

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Description : A fair coin is tossed three times. Let A, B and C be defined as follows: -Maths 9th

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Description : When a dice is rooled, find the probability of getting an even prime number.

Last Answer : When a dice is rooled, find the probability of getting an even prime number. A. `1/6` B. `1/3` C. `1/2` D. `5/6`

Description : If a dice is rooled, then the probability of getting a prime number is _______.

Last Answer : If a dice is rooled, then the probability of getting a prime number is _______.

Description : A dice is rolled, the probability that the number on the face showing up is greater than 6 is ______.

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Description : Now it was Ravi‘s turn. He rolled the dice. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is greater than 8? a. 1 b. 5/36 c. 1/18 d. 5/18

Last Answer : d. 5/18

Description : Rahul got next chance. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is equal to 7? a. 5/9 b. 5/36 c. 1/6 d. 0

Last Answer : c. 1/6

Description : Now it was Ravi‘s turn. He rolled the dice. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is less than or equal to 12? a. 1 b. 5/36 c. 1/18 d. 0

Last Answer : a. 1

Description : Rahul got next chance. What is the probability that he got the sum of the two numbers appearing on the top face of the dice is 13? a. 1 b. 5/36 c. 1/18 d. 0

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Description : When two dice are rolled, find the probability of getting a greater number on the first die than the one on the second, given that the sum should equal 8. a) 5/18 b) 1/18 c) 2/5 d) 1/5

Last Answer : c) 2/5

Description : Two dice are rolling simultaneously .What is the probability that the sum of the number on the two faces is divided by 5 Or 7. A) 13/36 B) 14/36 C) 11/36 D) 9/36 

Last Answer :  Answer: C) Clearly, n(S) = 6 x 6 = 36 Let E be the event that the sum of the numbers on the two faces is divided by 5or 7. Then,E = {(1,4),(1,6),(2,3),(2,5),(3,2),(3,4),(4,1),(4,3),(4,6),(5,2),(5,5),(6,1),(6,4)} n(E) = 11. Hence, P(E) = n(E)/n(S) = 11/36

Description : Twenty-seven solid iron spheres, -Maths 9th

Last Answer : (i) Volume of 27 solid sphere, each of radius, r = 27 x 4/3 πr3 = 36 πr3 According to statement, Volume of sphere of radius r' = Volume of 27 solid spheres ⇒ 4/3 π(r'3 ) = 36 πr3 ⇒ (r')3 = 27r3 = (3r)3 ⇒ r' = 3r ( ... πr'2 = 4 π(3r)2 = 36 πr2 ∴ S/S' = 4 πr2 /36 πr2 = 1/9 ⇒ S : S' = 1 : 9

Description : State and prove-line joining the midpoint of any two sides of a triangle is parallel to throw side and is equal to 1/2 of it -Maths 9th

Last Answer : Here, In △△ ABC, D and E are the midpoints of sides AB and AC respectively. D and E are joined. Given: AD = DB and AE = EC. To Prove: DE ∥∥ BC and DE = 1212 BC. Construction: Extend line segment DE to ... we have DF ∥∥ BC and DF = BC DE ∥∥ BC and DE = 1212BC (DE = EF by construction) Hence proved.

Description : State and prove-line joining the midpoint of any two sides of a triangle is parallel to throw side and is equal to 1/2 of it -Maths 9th

Last Answer : Here, In △△ ABC, D and E are the midpoints of sides AB and AC respectively. D and E are joined. Given: AD = DB and AE = EC. To Prove: DE ∥∥ BC and DE = 1212 BC. Construction: Extend line segment DE to ... we have DF ∥∥ BC and DF = BC DE ∥∥ BC and DE = 1212BC (DE = EF by construction) Hence proved.

Description : A and B throw a coin alternately till one of them gets a ‘head’ and wins the game. Find their respective probabilities of winning . -Maths 9th

Last Answer : Let A : Event of A getting a head ⇒ \(\bar{A}\) : Event of A not getting a head ∴ P(A) = \(rac{1}{2}\) and P(\(\bar{A}\)) = 1 - \(rac{1}{2}\) = \(rac{1}{2}\)Similarly, B : Event of B ... exclusive events, as either of them will win, P(B winning the game first) = 1 - \(rac{2}{3}\) = \(rac{1}{3}\).

Description : If you toss a die and it comes up with the number one 9 times in a row, what is the probability that it will come up with one on the next throw? -Riddles

Last Answer : One in six. A die has no memory of what it last showed.

Description : What standards do you think tennis players use when they throw one ball back from the three they get thrown by the ball boy/girl?

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Description : A computer program selects an integer in the set {k : 1 ≤ k ≤ 10,00,000} at random and prints out the result. This process is repeated 1 million times. What is the probability that the value k = 1 appears in the printout atleast once ? (A) 0.5 (B) 0.704 (C) 0.632121 (D) 0.68

Last Answer : (C) 0.632121