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

Three identical dice are rolled. The probability that same number will appear on each of them is -Maths 9th
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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, 6, 6)} ⇒ n(A) = 6 ∴ P(A) = \(rac{n(A)}{n(S)}\) = \(rac{6}{216}\) = \(rac{1}{36}\).
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Description : Five horses are in a race. Mr A. Selects two of the horses at random and bets on them. The probability that Mr A selected the winning horse is -Maths 9th

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Description : Find the probability that the three cards drawn from a pack of 52 cards are all black ? -Maths 9th

Last Answer : Number of ways in which three cards can be drawn from a pack of 52 cards n(S) = 52C3. Let A : Event of drawing all the three cards as black Then, n(A) = 26C3 (∵There are 26 black cards)∴ P(A ... (rac{^{26}C_3}{^{52}C_3}\) = \(rac{26 imes25 imes24}{52 imes51 imes50}\) = \(rac{2}{17}.\)

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Description : The letters of the word ‘SOCIETY’ are placed at random in a row. What is the probability that three vowels come together ? -Maths 9th

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Four boys and three girls stand in a queue for an interview. What is the probability that they will be in alternate positions ? -Maths 9th

Description : Four boys and three girls stand in a queue for an interview. What is the probability that they will be in alternate positions ? -Maths 9th

Last Answer : Total number of ways of arranging 4 boys and 3 girls, i.e., 7 people in a queue (row) = n(S) = 7! Let A : Event in which the 4 boys and 3 girls occupy alternate position. This is possible when the ... {4 imes3 imes2 imes1 imes3 imes2 imes1}{7 imes6 imes5 imes4 imes3 imes2 imes1}\) = \(rac{1}{35}.\)

If three natural numbersfrom 1 to 100 are selected randomly, then the probability that all are divisible by both 2 and 3 is -Maths 9th

Description : If three natural numbersfrom 1 to 100 are selected randomly, then the probability that all are divisible by both 2 and 3 is -Maths 9th

Last Answer : (c) \(rac{4}{1155}\)Let n(S) = Number of ways of selecting 3 numbers from 100 numbers = 100C3 Let E : Event of selecting three numbers divisible by both 2 and 3 from numbers 1 to 100 = Event of selecting three ... C_3}{^{100}C_3}\) = \(rac{16 imes15 imes14}{100 imes99 imes98}\) = \(rac{4}{1155}\).

A box contains 100 balls numbers from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability -Maths 9th

Description : A box contains 100 balls numbers from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability -Maths 9th

Last Answer : (d) \(rac{1}{4}\)The box contains 100 balls numbered from 1 to 100. Therefore, there are 50 even and 50 odd numbered balls. The sum of the three numbers drawn will be odd, if all three are odd or one is even and 2 are odd. ∴ Required probability = P(odd) × P(odd) × P(odd) + P(even) × P(odd) × P(odd)

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Description : Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with these vertices is equilateral equals : -Maths 9th

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If the three independent events E1, E2 and E3, the probability that only E1 occurs is α, E2 occurs -Maths 9th

Description : If the three independent events E1, E2 and E3, the probability that only E1 occurs is α, E2 occurs -Maths 9th

Last Answer : (c) 6Let \(x\), y, z be the probabilities of happening of events E1, E2 and E3 respectively. Then, \(\alpha\) = P (occurrence of E1 only) = x (1 - y) (1 - z) \(\beta\) = P (occurrence of E2 only) = (1 - \(x\)) y (1 - ... (x\) = 6z (From (i) and (ii))⇒ \(rac{x}{z}\) = 6 ⇒ \(rac{P(E_1)}{P(E_3)}\) = 6.

What is the probability of the occurrence of a number that is even or less than 3 when a fair die is rolled. a) 2/3 b)3/2 c)5/6 d)6/5

Description : What is the probability of the occurrence of a number that is even or less than 3 when a fair die is rolled. a) 2/3 b)3/2 c)5/6 d)6/5

Last Answer : Answer: A) Let the event of the occurrence of a number that is even be A' and the event of the occurrence of a number that is less than 3 be B'. We need to find P(A or B). P(A) = 3/6 (even numbers = 2,4,6) P(B) = 2/6 ( ... = P(A) + P(B) - P(A or B)  = 3/6 + 2/6 - 1/6 P(A or B) = 4/6=2/3