stats_ps4_winter24

Stats Problem Set #4 1. The gene that governs albinism has two forms (called alleles), which we denote by a and A . Each person has a pair of these genes, one inherited from each parent. A child inherits one of each parent’s two alleles, independently and with probability 0.5. Albinism is a recessive trait, so a person is albino only if the inherited pair is aa . Beth’s parents are not albino but she has an albino brother. Beth is not albino. What is the probability that Beth’s genetic type is AA given all of this information? (Round your answer to four decimal places. Remember to express your answer as a proportion.) 2. All of the information given in Problem #1 also holds for Problem #2. Beth is married to Bob, who is albino. Beth and Bob have one child and that child is not albino. What is the probability that Beth’s genetic type is Aa given this information and the information from Problem #1? (Round your answer to four decimal places. Remember to express your answer as a proportion.) -- - - - - - 113 Os 0 . 3333 # AaxAa O O Ha-AG - * & ⑳ ⑰ # an O Q 2 (0 . 6) - 10 . 05 It e 0 . 5833 0 . 5008 ⑰

3. Suppose that A and B are two events with P( A ) = 0.4, P( B ) = 0.3, and P( B | A )=0.5. What is P( A or B )? 4. Suppose that F and G are two events with P( F ) = 0.25, P( G ) = 0.5, and P( F | G )=0.6. What is P( F or G )? 5. This problem involves two distinct sets of events, which we label A 1 and A 2 and B 1 and B 2 . The events A 1 and A 2 are mutually exclusive and collectively exhaustive within their set. The events B 1 and B 2 are mutually exclusive and collectively exhaustive within their set. Intersections can occur between all events from the two sets. Given P ( A 1 ) = 0.7, P ( B 1 | A 1 ) = 0.2, and P ( B 1 | A 2 ) = 0.6, what is P ( A 1 | B 1 )? (Round your answer to four decimal places.) 6. This problem involves two distinct sets of events, which we label A 1 and A 2 and B 1 and B 2 . The events A 1 and A 2 are mutually exclusive and collectively exhaustive within their set. The events B 1 and B 2 are mutually exclusive and collectively exhaustive within their set. Intersections can occur between all events from the two sets. Given P ( A 1 ) = 0.2, P ( B 1 | A 1 ) = 0.8, and P ( B 1 | A 2 ) = 0.4, what is P ( A 2 | B 2 )? (Round your answer to four decimal places.)