1.Let A and B be events such that P(A) = 0.2, P(B) = 0.7, P (A U B) = 0.8. Find

a.P(AB)

b.P(A|B)

c.P(B|A)

2.You are off to soccer and wants to be the Goalkeeper but that depends on who is the coach today. With coach Dan, probability of being Goalkeeper is 0.7 and with coach Bob, probability of being Goalkeeper is 0.4. Probability of Dan being a coach today is 0.4. Draw tree diagram and find the probability that you will be Goalkeeper today.

3.100 women use a new pregnancy test, 44 of the women are actually pregnant. Of the women who are pregnant, 35 test positive. Of the women who are not pregnant, 8 of them test positive. Draw tree diagram and Calculate the probability for each event.

1.A randomly selected test is negative, given the woman is not pregnant

2.A randomly selected test is positive

3.A randomly selected test is from a woman who is pregnant given it is negative

4.A randomly selected test is incorrect (false-positive or false-negative)

4.Fiction Cruiseline offers three ways to exercise on their cruise ships. 73 of the 86 passengers participated in at least one method of exercise. 36 people went rock climbing, 44 people went ice skating, and 19 went to the fitness center. 14 people went rock climbing and ice skating, 11 people went rock climbing and to the fitness center, and 9 people went ice skating and to the fitness center. 8 participated in all 3 exercises. Calculate the probability for each given event.

1.A randomly selected passenger went rock climbing, given they did not go ice skating

2.A randomly selected passenger did not go rock climbing, given they did not go to the fitness center

3.A randomly selected passenger did not go ice skating, given they did at least two activities