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Question

Tickets numbered from 1 to 18 are mixed up together and then a ticket is drawn at random. Find the probability that the ticket has a number, which is a multiple of 2 or 3.

A
13
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B
35
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C
23
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D
56
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Solution

The correct option is C 23
S={1,2,3,4,18}n(S)=18E1={2,4,6,8,10,12,14,16,18}n(E1)=9E2={3,6,9,12,15,18}n(E2)=6(E1E2)=E3={6,12,18}n(E3)=3E=E1E2=E1+E2E3n(E)=9+63n(E)=12where E={2,3,4,6,8,9,10,12,14,15,16,18}P(E)=n(E)n(S)=1218=23

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