\fStay in school: In a recent school year in the state of Washington, there were 321,000 high school students. Of these, 153,000 were girls and 163,000 were boys. Among the gids, 29,600 dropped out of school, and among the boys, 10,100 dropped out. A student is chosen at random. Round the answers to four decimal places. (a) what is the probability that the student is male? (b) what is the probabiiity that the student dropped out? (c) what is the probability that the student is male and dropped out? (d) lGiven that the student is male, what is the probability that he dropped out? (e) Given that the student dropped out, what is the probability that the student is maie? GED: In a certain high schoolr the probability that a student drops out is 0.05, and the probability that a dropout gets a high schooi equivalency diploma (GED) is 0.26. What is the probability that a randomly selected student gets a GED? Round your answer to four decimal places, if necessary. The probability that the randomly selected student gets a GED is D. Defective components: A lot of 9 components contains 3 that are defective. Two components are drawn at random and tested. LetA be the event that the rst component drawn is defective, and let B be the event that the second component drawn is defective. Write your answer as a fraction or a decimal, rounded to four decimal places. (.3) Find P(A). (b) Find P(B IA). (-2) Find PM and B). (d) AreA and B independent? Explain. Lottery: Every clai,'r Jorge buys a lottery ticket. Each ticket has a probability of 0.2 of winning a prize. After ve days, what is the probability that Jorge has won at least one prize? Round your answer to four decimal places. The probability that Jorge has won at least one prize is D. LetA, B, and c be independent events with PM) :05: M3} = (11, and pm) = {13. Find pm and Band :3). P(A and3 and C)=E] K It} A fair ooin is tossed five times. What is the probability that all five tosses are tails? Write your answer as a fraction or a decimal, rounded to four decimal places. 111e, probability that all five tosses are tails is D. \fAn unfair ooin has probability 53 of landing heads. The coin is tossed four times. Iil'li'hat is the probability that it lands heads at least once? Round the answer to four decimal places. P{Lands heads at least once} = D \f\fGenetics: A geneticist is studying two genes. Each gene can be either dominant or recessive. A sample of 100 individuals is categorized as follows. Write your answer as a fraction or a decimal, rounded to four decimal places. Gene 2 Dominant Recessive Dominant 54 28 Gene 1 _ Recesswe 14 4 -:'5end data to Excel-r" (a) What is the probability that in a randomly sampled individual, gene 1 is recessive? (b) What is the probability that in a randomly sampled individual, gene 2 is recessive? (c) Given that gene 1 is recessive, what is the probability that gene 2 is recessive? (d) Two genes are said to be in linkage equilibrium if the event that gene 1 is recessive is independent of the event that gene 2 is recessive. Are these genes in linkage equilibrium
