question archive We have two events, A and B
We have two events, A and B
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We have two events, A and B. P(A) = 1l2 and HR) = 1/3. Hint: Draw Venn diagrams to help you think about the following possibilities: 1) if A and B are mutually exclusive, 2) if all the outcomes in B are also in A, 3) if there's partial but not complete overlap between events in A and events in B. (a) What is the smallest P(A and B) can be? (b) What is the largest P(A and B) can be? (c) What is the smallest P(A or B) can be? (d) What is the largest P(A or B) can be? I
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a) Smallest P(A and B) = 0
b) Largest P(A and B) = 1/3
c) Smallest P(A or B) = 1/2
d) Largest P(A or B) = 5/6
Step-by-step explanation
Solution Given P ( A ) =/ and p ( B ) = 1 For mutually exclusive events ( a) Smallest P ( A and B ) = Now consider the venn diagram A Since all outcomes in B are ly 4 theis 6 The largest p ( A andB ) = P B ) = 3 ( c ) The smallest p ( A or B ) = P( #+ P () - P (A NB ) Where p(AnB) is the largest 2 I ) The largest P ( A or B ) = P A ) ( P ( B ) - P ( AnB ) -sismallest = p ( A ) + P B ) - O = / + K - 0 = 5/6
