Katie C.

asked • 03/31/15

Compute the following conditional probabilities:

events E and F in a sample space S, but assume that Pr[E] = 0.45, Pr[F] = 0.45, and Pr[E∩ F] = 0.25.
Compute the following conditional probabilities:

(1) Pr[E | F] =

(2) Pr[F | E] =

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Jon P. answered • 03/31/15

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The formula for conditional probability is pretty simple:
 
P (A | B) = P (A∩B) / P (B)
 
So in these cases:
 
1) Pr [E | F] = Pr (E∩F) / Pr (F) = 0.25 / 0.45 = 0.556
 
2) Pr [F | E] = Pr (E∩F) / Pr (E) = 0.25 / 0.45 = 0.556
 
So they're both the same, 0.556.
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Katie C.

Thank you!! Could you help me with these problems too? 
 
For this problem, assume that the committee contains 10 men and 5 women and that three are selected at random for a subcommittee.
What is the probability that the subcommittee consists of 2 men and 1 woman, given that it contains both men and women?
 
Assume that you have 6 red balls and 7 blue balls from which randomly to select two without replacement.
(1) What is the probability that exactly one blue ball is chosen?

(2) What is the probability that the second ball is blue given that at least one of the balls is blue?
 
Assume that each bag contains 5 balls. Bag a contains 4 red and 1 white, while bag b contains 1 red, 1 white, and 3 blue. You randomly select one ball from bag a, note the color, and place the ball in bag b. You then select a ball from bag b at random and make note of its color.
(1) What is the probability that both balls are red?

(2) What is the probability that both balls are red given that the first ball you drew was red?
 
 
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03/31/15

Jon P.

tutor
I think your best bet is to post each of them as a separate question, not as a comment to this question.  Then all the tutors will see them and you have more chance of getting answers.
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03/31/15

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