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Question

A number is chosen at random from the set {1,2,3,,2000}. Let p be the probability that the chosen number is a multiple of 3 or a multiple of 7. Then the value of 500p is

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Solution

E= A number which is multiple of 3 or multiple of 7
Let A= Set of numbers divisible by 3
A={3,6,9,,1998}
n(A)=666
B= Set of numbers divisible by 7
B={7,14,21,,1995}
n(B)=285
AB={21,42,63,,1995}
n(AB)=95
Now,
n(E)=n(A)+n(B)n(AB)
n(E)=666+28595
n(E)=856
Required probability
p=8562000
500p=8564=214

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