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Use overlap bounds before adding the conditional information

For events A and B, P(A)=5/8P(A)=5/8 and P(B)=2/3P(B)=2/3.

(i) Find the greatest and least possible values of P(A∩B)P(A\cap B).

It is given in addition that P(A′∣B′)=3/8P(A'\mid B')=3/8.

(ii) Find P(A′∩B′)P(A'\cap B').

(iii) Find P(A∪B)P(A\cup B).

(iv) Determine if A and B are independent.

(v) Another event C satisfies P(C)=3/8P(C)=3/8, P(A∩C)=P(B∩C)=1/4P(A\cap C)=P(B\cap C)=1/4 and P(A∪B∪C)=11/12P(A\cup B\cup C)=11/12. Find P(A∩B∩C)P(A\cap B\cap C).

[2016/RI/P2/10]

CJC · Discussion · Question 6

For the least intersection, make the union as large as possible.

Read the worked solution