16.5 Working with Conditional Probability

Use the probability tree to find the specified probabilities. a) P(Y) b) P(B|Y) c) P(B|Z) d) P(X and A) e) P(Y and A) f) P(Z and A) g) P(A) h) P(B) i) P(X|A) j) P(Z|A) a).2 b).6 c).7 d).1 e).O8 f).09 g).27 h).73 i).37 j).33

A. Draw a tree diagram that shows the given facts. B. Find the probability of picking a white ball. C. If a white ball is picked, what is the probability that it came from Jar A? Jar B. Jar A contains 1 red, 2 white, and 3 green balls. Jar B contains 4 red and 5 white balls. A die is rolled. If a “1” or a “6” comes up a ball is randomly picked from Jar A. Other wise, a ball is randomly picked from Jar B.

NNBW AR G RW A. Draw a tree diagram that shows the given facts. JAR

Find the probability of picking a white ball P(choosing 1 or 6 and picking white) + P(not choosing 1 or 6 and picking white)

Find the probability of picking a white ball

If a white ball is picked, what is the probability that it came from Jar A?

During a flu epidemic, 35% of a school’s students have the flu. Of those with the flu, 90% have high temperatures. However, a high temperature is possible for people without the flu. It was estimated that 12% had a high temperature that did NOT have the flu. Make a tree diagram NF NT FT T SICK

What percent of students have a high temperature? P(F and T) + P(NF and T) (0.35)(0.90) + (0.65)(0.12) =0.393

If a student has a high temperature, what is the probability that the student has the flu?

A high school basketball team leads at halftime in 60% of the games in a season. The team wins 80% of the time when they have the halftime lead, but only 10% of the time when they do not. What is the probability that the team wins a particular game during the season? The team won their game, what is the probability they were NOT leading at halftime? P(L and W) + P(NL and W) (0.60)(0.80) + (0.40)(0.10) =0.52

Homework Textbook p #1, 2, 5, 7, 9