Question

Question 10 Your answer is CORRECT. This is a written question, worth 14 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 1023 Given: P(E) = 0.38, P(F) = 0.68, and P(E U F) = 0.82 Part a: Find P(En F). Part b: Find P( EF). Part : Find P(FE). Part d: Are the events E and F independent? a)" I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem.

Answer 1

Given, P(E)=0.38 , P(F)= 0.68 and P(E U F) = 0.82

a)we know,

P(E $\cap$ F) = P(E) + P(F) - P ( E U F)

= 0.38 + 0.68 - 0.82 = 0.24 (ans)

b) we know, P( E | F) = P( E $\cap$ F) / P(F)

= 0.24 / 0.68 = 0.35 (ans)

c) we know, P ( F | E) = P( F $\cap$ E) / P( E)

= 0.24/0.38 = 0.63

d) E and F are independent iff P( E $\cap$ F) = P( E) P( F)

P(E) P(F) = 0.38*0.68 = 0.26 $\neq$ P( E $\cap$ F) = 0.24

Hence, E and F are not independent.

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