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If the probability of a student joining the debate team is 0.5, the probability of joining...

If the probability of a student joining the debate team is 0.5, the probability of joining the drama club is 0.2, and the probability of joining the debate team or drama club is 0.58, what is the probability of a student joining the debate team and drama club?

Math   Statistics-And-Probability   
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Answer #1

P(A) = P[a student joining the debate team ]= 0.5

P(B) = P[a student joining the drama club ] = 0.2

P(A or B) = P[a student  joining the debate team or drama club ] = 0.58

P(A and B) = P[a student  joining the debate team and  drama club ]

Addition rule of probability

P(A or B) = P(A) + P(B) - P(A and B)

Substitute here given values

=> 0.58 = 0.5 + 0.2 - P(A and B)

=> P(A and B) = 0.12

P(A and B) = P[a student  joining the debate team and  drama club ] = 0.12
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