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Questions Pg-76, , Question 1., , In class 10A, there are 20 boys and 20 girls. In 10B, there are 15 boys and 25 girls. One, student Is to be selected from each class., , i) What is the probability of both being girls?, li) What Is the probability of both being boys?, iii) What is the probability of one boy and one girl?, , iv) What is the probability of at least one boy?, , , , , , , , , , Answer:, Class Boys | Girls, 10A 20 20 40, 10B 15 25 40, Total 35 45 80, , , , , , , , , , , , , , Total number of students = 80, i. Probability of both being girl., , For both being a girl i.e. girl is selected from class 10A and another girl is selected, from class 10B, , Total number of girls = 45, , __ __ Total number of girls, Probability of both being girls Total number of students, , = 0.5625

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ii. Probability of both being boys, , For both being a boy i.e. boy is selected from class 10A and another boy is selected, from class 10B, , Total number of boys = 35, , __ _ Total number of boys, Probability of both being boys Total number of students, , _35 = 7, ~ 80 16, = 0.4375, , iii, Probability of one boy and one girl, , For one boy and one girl, a boy is selected from class 10A and a girl from class 10B or, vice a versa., , i.e. P (boy from class 10A) x P (girl from class 10B) +, , P (girl from class 10A) x P (boy from class 10B), 20. 25 20. 15, Gaia) GD, , 500 300, (+28), = 1600 1600, , MI, Nie

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iv. Probability of at least one boy., , For at least one boy means one boy and another girl, or both boy., , In this, one boy and other girl can occur in two ways:, , 1st boy and 2nd girl or the other way round., , (20 x 25) + (20 x 15), , = 500 + 300, , = 800, , “. the possibility is 0.50 (obtained in previous part), , We have already seen the possibility of both the boys in above solved parts i.e., probability of both boys is 0.4375, , “. Probability of at least one boy = 0.50 + 0.4375, , = 0.9375

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Question 2., , One is asked to say a two-digit number., i) What is the probability of both digits being the same?, ii) What is the probability of the first digit being larger?, , iii) What is the probability of the first digit being smaller?, , Answer:, , Total number of two -digit numbers = 90, , i. Probability of both digits being the same, Total number of numbers having same digit = 9, Probability of both digits being same, , _ Total number of numbers having same digit, ~ Total number of two — digit numbers, , , , 9 I, 90 10, ii. Probability of first digit being larger, , Total number of numbers having first digit larger = 45, , 10, 20, 21, 30, 31, 32, 40, 41, 42, 43, 50, 51, 52, 53, 54, 60, 61, 62, 63, 64, 65, 70, 71, 72,, 73, 74, 75, 76, 80, 81, 82, 83, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 96, 97, 98.

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Probability of first digit being larger, , , , _ Total number of numbers having first digit larger, - Total number of two — digit number, , 1, , 45, ~ 90, , iii. Probability of first digit being smaller, Total number of numbers having first digit smaller = 36, , 12, 13, 14, 15, 16, 17, 18, 19, 23, 24, 25, 26, 27, 28, 29, 34, 35, 36, 37, 38, 39, 45, 46, 47,, 48, 49, 56, 57, 58, 59, 67, 68, 69, 78, 79, 89., , Probability of first digit being smaller, , _ Total number of numbers having first digit smaller, - Total number of two — digit number, , , , = 0.25