Question

a.) Lactose intolerance causes difficulty digesting dairy products that contain lactose (milk sugar). It is particularly common among people of African and Asian ancestry. In the United States (ignoring other groups and people who consider themselves to belong to more than one race), 82% of the population is white, 14% is black, and 4% is Asian. Moreover, 15% of whites, 70% of blacks, and 90% of Asians are lactose intolerant.

(i) What percent of the entire population is lactose intolerant? (Enter your answer rounded to one decimal place.)

percent of the population who are lactose intolerant = ____%

(ii) What percent of people who are lactose intolerant are Asian? (Enter your answer rounded to two decimal places.)

percent of people who are lactose intolerant are Asian = ____%

b.)

About 4% of children in the United States are allergic to peanuts. Choose three children at random and let the random variable ?X be the number in this sample who are allergic to peanuts. The possible values ?X can take are 0,1,2,and 3.0,1,2,and 3.

What is the conditional probability that exactly two of the children will be allergic to peanuts, given that at least one of the three children suffers from this allergy?

Round your answer to six decimal places.

?(?=2∣?≥1)=P(X=2∣X≥1)=

c.)

A player serving in tennis has two chances to get a serve into play. If the first serve is out, the player serves again. If the second serve is also out, the player loses the point. Observe the probabilities based on four years of the Wimbledon Championship.

?(1st serve in)=0.59P(1st serve in)=0.59

?(win point | 1st serve in)=0.73P(win point | 1st serve in)=0.73

?(2nd serve in | 1st serve out)=0.86P(2nd serve in | 1st serve out)=0.86

?(win point | 1st serve out and 2nd serve in)=0.59P(win point | 1st serve out and 2nd serve in)=0.59

Make a tree diagram for the results of the two serves and the outcome, win or lose, of the point. The branches in your tree have different numbers of stages depending on the outcome of the first serve.

What is the probability that the serving player wins the point? Report your answer to four decimal places.

Answer 1