A box contains 15 balls bearing numbers 1, 2, 3, …, 14, 15 respectively. A ball is drawn at random from the box. Find the probability that the number on the ball is:
(i) an even number
(ii) a number divisible by 5
(iii) the number 6
(iv) a number lying between 8 and 12
(v) a number greater than 9
(vi) a number less than 6

Question

A box contains 15 balls bearing numbers 1, 2, 3, …, 14, 15 respectively. A ball is drawn at random from the box. Find the probability that the number on the ball is:
(i) an even number
(ii) a number divisible by 5
(iii) the number 6
(iv) a number lying between 8 and 12
(v) a number greater than 9
(vi) a number less than 6

KnowledgeBoat · Accepted Answer

Given, Balls in the box are numbered {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15} Total number of outcomes = 15 (i) Let A be the event of getting an even number, then A = {2, 4, 6, 8, 10, 12, 14} ∴ The number of favourable outcomes to the event A = 7 P(A) = Hence, the probability of getting an even number is . (ii) Let B be the event of getting a number divisible by 5, then B = {5, 10, 15} ∴ The number of favourable outcomes to the event B = 3 P(B) = Hence, the probability of getting a number divisible by 5 is . (iii) Let C be the event of getting the number 6, then C = {6} ∴ The number of favourable outcomes to the event C = 1 P(C) = Hence, the probability of getting the number 6 is . (iv) Let D be the event of getting a number between 8 and 12, then D = {9, 10, 11} ∴ The number of favourable outcomes to the event D = 3 P(D) = Hence, the probability of getting a number lying between 8 and 12 is . (v) Let E be the event of getting a number greater than 9, then E = {10, 11, 12, 13, 14, 15} ∴ The number of favourable outcomes to the event E = 6 P(E) = Hence, the probability of getting a number greater than 9 is . (vi) Let F be the event of getting a number less than 6, then F = {1, 2, 3, 4, 5} ∴ The number of favourable outcomes to the event F = 5 P(F) = Hence, the probability of getting a number less than 6 is .

Mathematics

Probability

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