Question

38. Let E and F be events with P(E) = .3, P(F) = .6, and P(E...

38. Let E and F be events with P(E) = .3, P(F) = .6, and P(E ∪ F) = .7. Find (a) P(E ∩ F) (b) P(E|F) (c) P(F|E) (d) P(Ec ∩ F) (e) P(Ec |F)

answers:  a. .2 b. .5 c. .67 d. .4 e. Please show work how to get these answers and include venn diagram thank you

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

P(E) = 0.3

P(F) = 0.6

P(E U F) = 0.7

a) P(E F) = P(E) + P(F) - P(E U F)

= 0.3 + 0.6 - 0.7

= 0.2

b) P(E | F) = P(E F)/P(F)

= 0.2/0.6

= 0.3333

c) P(F | E) = P(E F)/P(E)

= 0.2/0.3

= 0.6667

d) P(Ec F) = P(F) - P(E F)

= 0.6 - 0.2

= 0.4

e) P(Ec | F) = P(Ec F)/P(F)

= 0.4/0.6

= 0.6667

Venn Diagram

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