Thank you i advance. Consider two events A and B with Pr(A) =0.4 and Pr(B)=0.7 .

Question

Thank you i advance. Consider two events A and B with Pr(A) =0.4 and Pr(B)=0.7 .Determine the maximum and minimum possible values of Pr(A intercectB) and the conditions under which each of these values isattained. Thank you i advance. Consider two events A and B with Pr(A) =0.4 and Pr(B)=0.7 .Determine the maximum and minimum possible values of Pr(A intercectB) and the conditions under which each of these values isattained.

Explanation / Answer

P(A union B) = P(A) +P(B) - P(AintersectB) Max value of P(A union B ) = 1 If P(A union B) is max then since P(A) and P(B) are fixedP(AintersecB) must be minimum P(AintersecB) = P(A) +P(B)-P(A union B) =0.4+0.7-1 =0.1--->min value occurs when P(A union B ) = 1, i.e when eitherA or B must occur Also maximum value of P(A intersec B) = 1 occurs when P(AUB) =minimum ; In this case, P(A union B) = P(A) + P(B)-1 = 0.7 + 0.4 -1--> Hence max value occurs when Probability of either A or Boccuring is 0.1

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