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2.3 Probability

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Question 54

The events X X\,X and Y Y\,Y are such that P(X)=0.6P(X) = 0.6P(X)=0.6, P(Y)=0.25P(Y) = 0.25P(Y)=0.25 and P(X∣Y)=0.4P(X|Y) = 0.4P(X∣Y)=0.4.

a.

Find P(X∩Y)P(X \cap Y)P(X∩Y).

[2]
b.

Find P(Y′∣X)P(Y'|X)P(Y′∣X).

[3]
c.

Find P(X′∪Y)P(X' \cup Y)P(X′∪Y).

[2]
d.

Determine whether the events X X\,X and Y Y\,Y are independent, give a reason for your answer.

[3]

2.3 Probability Questions

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