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

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
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1 Answer

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), (3, 5), (3, 6)} ⇒ n(A) = 6 B = {(1, 3), (2, 3), (3, 3), (4, 3), (5, 3), (6, 3)} ⇒ n(B) = 6 A ∩ B = {(3, 3)} ⇒ n(A ∩ B) = 1 ∴ P(A) = \(rac{n(A)}{n(S)}\) = \(rac{6}{36}\), P(B) = \(rac{n(B)}{n(S)}\) = \(rac{6}{36}\), P (A ∩ B) = \(rac{n(A\cap{B})}{n(S)}\) = \(rac{1}{36}\)∴ Required probability = P(Throwing a 3 with at least one of the dice)= P(A) + P(B) – P(A ∩ B)= \(rac{6}{36}\) + \(rac{6}{36}\) - \(rac{1}{36}\) = \(rac{11}{36}\).
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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

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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) = \(rac{n(A)}{n(S)}\) = \(rac{11}{36}\).

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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The probability that in the random arrangement of the letters of the word ‘UNIVERSITY’the two I‘s do not come together is -Maths 9th

Description : The probability that in the random arrangement of the letters of the word ‘UNIVERSITY’the two I‘s do not come together is -Maths 9th

Last Answer : (b) \(rac{4}{5}\)Let S be the sample space. Then, n(S) = Total number of waysin which the letters of the word UNIVERSITY' can be arranged = \(rac{10!}{2!}\) (∵ There are 2I s) ... ! imes36}{rac{10!}{2!}}\) = \(rac{ ot8! imes36 imes2!}{10 imes9 imes ot8!}\) = \(rac{4}{5}\).

A bag contains 5 green and 7 red balls, out of which two balls are drawn at random. What is the probability that they are of the same colour ? -Maths 9th

Description : A bag contains 5 green and 7 red balls, out of which two balls are drawn at random. What is the probability that they are of the same colour ? -Maths 9th

Last Answer : (d) \(rac{31}{66}\)Total number of balls in the bag = 12 (5 Green + 7 Red) Let S be the sample space of drawing 2 balls out of 12 balls.Thenn(S) = 12C2 = \(rac{12 imes11}{2}\) = 66∴ Let A : Event of drawing two red balls⇒ ... \(rac{n(B)}{n(S)}\) = \(rac{21}{66}\) + \(rac{10}{66}\) = \(rac{31}{66}\).

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

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