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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 310
The 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,
AB = {35}i.e., n(AB) = 1Thus, P(AB) = 140

By addition rule of probability,
P(AB) = P(A)+P(B)P(AB)= 840 + 540 140= 1240= 310
Therefore, probability that the selected number is divisible by 5 or 7 is 310.

Mathematics

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