stats_ps3_winter24

Stats Problem Set #3 1. Each of us has an ABO blood type, which describes whether two characteristics called A and B are present. Every human being has two blood type alleles (gene forms), one inherited from our mother and one from our father. Each of these alleles can be A, B, or O. Which two we inherit determines our blood type. Here is a table that shows what our blood type is for each combination of two alleles: Alleles inherited Blood type A and A A A and B AB A and O A B and B B B and O B O and O O We inherit each of a parent’s two alleles with probability 0.5. We inherit independently from our mother and father. Elise has alleles A and B. John has alleles A and B. They have three children. What is the probability that all of their children have the same blood type? (Round your answer to four decimal places if necessary. Remember to express your answer as a proportion.) 2. Use the table from Question #1. We inherit each of a parent’s two alleles with probability 0.5. We inherit independently from our mother and father. Sally has alleles A and O. Sam has alleles A and O. They have four children. What is the probability that all of their children have the same blood type? (Round your answer to four decimal places if necessary. Remember to express your answer as a proportion.) - - -- - Jahn P(al3 sme) = P(aNA) + PCwAB) + PfalB) = (0 . 25)3 + (0 . 5)" + (0 . 20) = 0 . 15625 ABB) An e I - - 10 . 1563 PCA) = 0 20 PCAM) , O e - > -- - - Pall & same) = P Call A) + P Call Of = 0 . 3203/25 #03 sald · a d = (0 . 75). + (0 25) * PA = 0

2 3. The probability that a randomly selected American has disease Z is 0.03. If 75 people are randomly selected from the population, what is the probability that at least 1 of them has disease Z ? (Round your answer to four decimal places. Remember to express your answer as a proportion.) 4. Twenty-four percent of the American adult population supports candidate Green. An SRS of 13 adults asks if they agree with the statement “I support candidate Green .” What is the probability that at least 2 of those surveyed would agree with that statement? (R ound your answer to four decimal places. Remember to express your answer as a proportion.) - - -° = A P = Call not z) = (0 . 97)30 Plat let 1z) = D - (0 . 979 = - > 0 . 898/68986 - 10 . 8962 - - - # = Plexachid Dagest Planact/6 / agrees) + ↑ (at reast I agree 1 = (8) [10 . 28)c076("] + (vi) [co . 28)"Co . 76) : 2] + a

4 7. The sample space contains 4 As and 5 Bs. What is the probability that a randomly selected set of 3 will include 1 A and 2 Bs? (R ound your answer to four decimal places. Remember to express your answer as a proportion.) 8. The sample space contains 3 As and 6 Bs. What is the probability that a randomly selected set of 4 will include 2 As and 2 Bs? (R ound your answer to four decimal places. Remember to express your answer as a proportion.)

5 9. A personnel officer has 6 candidates to fill 3 similar positions. Of the 6 candidates, 4 are male and 2 are female. If every combination of candidates is equally likely to be chosen, what is the probability that no women will be hired? (R ound your answer to four decimal places. Remember to express your answer as a proportion.) 10. Fifty-eight percent of the American adult population supports candidate Adams and forty-two percent opposes candidate Adams. An SRS of five adults asks if they agree with the statement “I support candidate Adams.” What is the probability that a majority of those surveyed would disagree with that statement? (R ound your answer to four decimal places. Remember to express your answer as a proportion.)