A school band sold 30 raffle tickets, each labeled with a number from 1 to 30. One winning ticket will be drawn. What is the probability that the number of the winning ticket will be a multiple of 4 or the number 19?

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Answer 1 · 2016-07-22T11:49:22

The reqd. Prob.#=4/15~=0.27#.#.

We will use Set Theory Approach of Probability to solve this problem.

Let #U#= the Sample Space, consisting of all possible outcomes.

Clearly, #U={1,2,3....,30}#, so that,

no. of elements in #U=n(U)=30#.

Let #A#= the event that winning ticket bears a no. multiple of #4#,

and, #B#= the event that the winning ticket has the no. #19#.

#:.A={4,8,12,16,20,24,28}, and, B={19}#, so that

#AnnB=phi#, meaning that #a &B# are mutually exclusive events.

#:. P(AnnB)=0#

As, #n(A)=7, n(B)=1#, we have,

#P(A)=(n(A))/(n(U))=7/30, and P(B)=1/30#

Now, the Reqd. Prob.#=P(AuuB)=P(A)+P(B)-P(AnnB)#

#=7/30+1/30-0=8/30=4/15~=0.27#.

Hope, this is Helpful! Enjoy Maths.!