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Question

# A number is randomly selected from the first 40 natural numbers. What is the probability that the selected number is divisible by 5 or 7?

A
820
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B
1740
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C
720
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D
310
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Solution

## The correct option is D 310The sample space for the given experiment is S = {1, 2, 3, 4, ...., 39, 40} n(S) = 40 Let A be the event that the number selected is divisible by 5. Then A = {5, 10, 15, 20, 25, 30, 35, 40} n(A) = 8 ⇒P(A) = 840 Let B be the event that the number selected is divisible by 7. Then B = {7, 14, 21, 28, 35} n(B) = 5 ⇒P(B) = 540 Now, A∩B = {35}i.e., n(A∩B) = 1Thus, P(A∩B) = 140 By addition rule of probability, P(A∪B) = P(A)+P(B)−P(A∩B)= 840 + 540− 140= 1240= 310 Therefore, probability that the selected number is divisible by 5 or 7 is 310.

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