1. -150 points TEAFM2 4.7.002 My Notes Find P(FI B) and P(EI A) using the tree d

Question

1. -150 points TEAFM2 4.7.002 My Notes Find P(FI B) and P(EI A) using the tree diagram. (Round your answers to three decimal places.) PE I A) 0.35 0.6 0.65 0.65A 0.4 0.35 2. -150 points TEAFM2 4.7.006. My Notes An un contains 3 white balls and 7 red balls. A second urn contains 6 white bals and 4 red balls. An urn is selected, and a bll is randomly drawn from the selected urn. The probability of selecting the first urn is 0.6. If the ball is white, find the probability that the second urn was selected. (Round your answer to three decimal places.)

Explanation / Answer

Question 1

P(Fl B)

it is bayes theorem question

first we will find P(B) = 0.6 * 0.65 + 0.4 * 0.35 = 0.53

Here

P(F l B) = (0.4 * 0.35)/ 0.53 = 0.2642

P(E l A)

Now again

P(A) = 0.6 * 0.35 + 0.4 * 0.65 = 0.47

P(E l A) = (0.6 * 0.35)/ 0.47 = 0.4468

Question 2

Here white balls= 3

Red balls = 7

Second urn contains

WHite balls = 6

Red balls = 4

Pr(First urn) = 0.6

Pr(Second urn) = 1 - 0.6 = 0.4

Selected ball = White

so

Here we want to know

Pr(Second urn l White)

so again by bayes theorem we will find the probability of getting white first

Pr(White ball) = Pr(Urn first chosen) * Pr(White ball) + Pr(Second urn chosen) * Pr(White ball)

= 0.6 * 3/10 + 0.4 * 6/10

= 0.42

Pr(Second urn l White ball) = (0.4 * 0.6)/ 0.42 = 0.571

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