EBK FIRST COURSE IN PROBABILITY, A
10th Edition
ISBN: 9780134753683
Author: Ross
Publisher: VST
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Chapter 3, Problem 3.66P
Genes relating to albinism are denoted by A and a. Only those people who receive the a gene from both parents will be albino. Persons having the gene pair A, a are normal in appearance and, because they can pass on the trait to their offspring, are called carriers. Suppose that a normal couple has two children, exactly one of whom is an albino. Suppose that the nonalbino child mates with a person who is known to be a carrier for albinism.
a. What is the
b. What is the conditional probability that their second offspring is an albino given that their firstborn is not?
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Some traits of plants and animals depend on inheritance of a single gene. This is called Mendelian inheritance, after Gregor Mendel (1822-1884). 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
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B and B
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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.
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green divided by bluegreen/blue,
which consists of the pair of alleles that determine
eye coloreye color,
and each parent contributes one of those alleles to a child. Assume that if the child has at least one
greengreen
allele, that color will dominate and the child's
eye coloreye color
will be
greengreen.
a. List the different possible outcomes. Assume that these outcomes are equally likely.
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blue divided by blueblue/blue
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c. What is the probability that the child will have
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a. List the possible outcomes.
A.
green divided by green comma green divided by blue comma and blue divided by bluegreen/green, green/blue, and blue/blue
B.
green divided by blue and blue divided by greengreen/blue and blue/green
C.
green divided by green and blue divided by bluegreen/green and blue/blue
D.
green divided by green…
Chapter 3 Solutions
EBK FIRST COURSE IN PROBABILITY, A
Ch. 3 - Two fair dice are rolled. What is the conditional...Ch. 3 - If two fair dice are rolled, what is the...Ch. 3 - Use Equation (2.1) to compute in a hand of bridge...Ch. 3 - What is the probability that at least one of a...Ch. 3 - An urn contains 6 white and 9 black balls. If 4...Ch. 3 - Consider an urn containing 12 balls, of which 8...Ch. 3 - The king comes from a family of 2 children. What...Ch. 3 - A couple has 2 children. What is the probability...Ch. 3 - Consider 3 urns. Urn A contains 2 white and 4 red...Ch. 3 - Three cards are randomly selected, without...
Ch. 3 - Two cards are randomly chosen without replacement...Ch. 3 - Suppose distinct values are written on each of 3...Ch. 3 - A recent college graduate is planning to take the...Ch. 3 - Suppose that an ordinary deck of 52 cards (which...Ch. 3 - An urn initially contains 5 white and 7 black...Ch. 3 - An ectopic pregnancy is twice as likely to develop...Ch. 3 - Ninety-eight percent of all babies survive...Ch. 3 - In a certain community, 36 percent of the families...Ch. 3 - A total of 46 percent of the voters in a certain...Ch. 3 - A total of 4.8 percent of the women and 37 percent...Ch. 3 - Fifty-two percent of the students at a certain...Ch. 3 - A total of 500 married working couples were polled...Ch. 3 - A red die, a blue die, and a yellow die (all six...Ch. 3 - Urn I contains 2 white and 4 red balls, whereas...Ch. 3 - Twenty percent of Bs phone calls are with her...Ch. 3 - Each of 2 balls is painted either black or gold...Ch. 3 - The following method was proposed to estimate the...Ch. 3 - Suppose that 5 percent of men and 0.25 percent of...Ch. 3 - All the workers at a certain company drive to work...Ch. 3 - Suppose that an ordinary deck of 52 cards is...Ch. 3 - There are 15 tennis balls in a box, of which 9...Ch. 3 - Consider two boxes, one containing 1 black and 1...Ch. 3 - Ms. Aquina has just had a biopsy on a possibly...Ch. 3 - A family has j children with probability pj, where...Ch. 3 - On rainy days, Joe is late to work with...Ch. 3 - In Example 31, suppose that the new evidence is...Ch. 3 - With probability .6, the present was hidden by...Ch. 3 - Stores A, B, and C have 50, 75, and 100 employees,...Ch. 3 - a. 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Two of...Ch. 3 - Suppose there are two coins, with coin 1 landing...Ch. 3 - In a 7 game series played with two teams, the...Ch. 3 - A parallel system functions whenever at least one...Ch. 3 - If you had to construct a mathematical model for...Ch. 3 - In a class, there are 4 first-year boys, 6...Ch. 3 - Suppose that you continually collect coupons and...Ch. 3 - A simplified model for the movement of the price...Ch. 3 - Suppose that we want to generate the outcome of...Ch. 3 - Independent flips of a coin that lands on heads...Ch. 3 - The color of a persons eyes is determined by a...Ch. 3 - Genes relating to albinism are denoted by A and a....Ch. 3 - Barbara and Dianne go target shooting Suppose that...Ch. 3 - A and B are involved in a duel. 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A starts and continues...Ch. 3 - Die A has 4 red and 2 white faces, whereas die B...Ch. 3 - An urn contains 12 balls, of which 4 are white....Ch. 3 - Repeat Problem 3.87 when each of the 3 players...Ch. 3 - Let S={1,2,...,n} and suppose that A and B are,...Ch. 3 - Consider an eight team tournament with the format...Ch. 3 - Consider Example 2a, but now suppose that when the...Ch. 3 - In Example 5, what is the conditional probability...Ch. 3 - In Laplace s rule of succession (Example 5e ), are...Ch. 3 - A person tried by a 3-judge panel is declared...Ch. 3 - Each of n workers is independently qualified to do...Ch. 3 - Suppose in the preceding problem that n=2 and that...Ch. 3 - Each member of a population of size n is,...Ch. 3 - Show that if P(A)0, then P(ABA)P(ABAB)Ch. 3 - Prob. 3.2TECh. 3 - Consider a school community of m families, with ni...Ch. 3 - A ball is in any one of n boxes and is in the ith...Ch. 3 - a. Prove that if E and F are mutually exclusive,...Ch. 3 - Prove that if E1,E2,...,En are independent events,...Ch. 3 - a. An urn contains n white and m black balls. The...Ch. 3 - Let A, B, and C, be events relating to the...Ch. 3 - Consider two independent tosses of a fair coin....Ch. 3 - Two percent of women age 45 who participate in...Ch. 3 - In each of n independent tosses of a coin, the...Ch. 3 - Show that 0ai1,i=1,2,..., then...Ch. 3 - The probability of getting a head on a single toss...Ch. 3 - Suppose that you are gambling against an...Ch. 3 - Independent trials that result in a success with...Ch. 3 - Independent trials that result in a success with...Ch. 3 - Suppose that n independent trials are performed,...Ch. 3 - Let Q. denote the probability that no run of 3...Ch. 3 - Consider the gamblers ruin problem, with the...Ch. 3 - Prob. 3.20TECh. 3 - The Ballot Problem. In an election, candidate A...Ch. 3 - As a simplified model for weather forecasting,...Ch. 3 - A bag contains a white and b black balls. Balls...Ch. 3 - A round-robin tournament of n contestants is a...Ch. 3 - Prove directly thatP(EF)=P(EFG)P(GF)+P(EFGC)P(GCF)Ch. 3 - Prove the equivalence of Equations (5.11) and...Ch. 3 - Prob. 3.27TECh. 3 - Prove or give a counterexample, if E1 and E2 are...Ch. 3 - In Laplaces rule of succession (Example 5e ), show...Ch. 3 - In Laplaces rule of succession (Example 5e),...Ch. 3 - Suppose that a nonmathematical, but...Ch. 3 - In a game of bridge, West has no aces What is the...Ch. 3 - Prob. 3.2STPECh. 3 - How can 20 balls, 10 white and 10 black, be put...Ch. 3 - Prob. 3.4STPECh. 3 - An urn has r red and w white balls that are...Ch. 3 - An urn contains b black balls and r red balls. One...Ch. 3 - A friend randomly chooses two cards, without...Ch. 3 - Show that P(HE)P(GE)=P(H)P(G)P(EH)P(EG). Suppose...Ch. 3 - You ask your neighbor to water a sickly plant...Ch. 3 - Six balls are to be randomly chosen from an urn...Ch. 3 - A type C battery is in working condition with...Ch. 3 - Prob. 3.12STPECh. 3 - Balls are randomly removed from an urn that...Ch. 3 - A coin having probability .8 of landing on heads...Ch. 3 - In a certain species of rats, black dominates over...Ch. 3 - a. In Problem 3.70b, find the probability that a...Ch. 3 - For the k-out-of-n system described in Problem...Ch. 3 - Prob. 3.18STPECh. 3 - Prob. 3.19STPECh. 3 - Suppose that there are n possible outcomes of a...Ch. 3 - If A flips vand B flips n fair coins, show that...Ch. 3 - Prove or give counterexamples to the following...Ch. 3 - Let A and B be events having positive probability....Ch. 3 - Rank the following from most likely to least...Ch. 3 - Two local factories, A and B, produce radios. Each...Ch. 3 - Show that if P(AB)=1, then P(BCAC)=1Ch. 3 - Prob. 3.27STPECh. 3 - A total of 2n cards, of which 2 are aces, are to...Ch. 3 - There are n distinct types of coupons, and each...Ch. 3 - Show that for any events E and F,P(EEF)P(EF) Hint:...Ch. 3 - a. If the odds of A is 23, what is the probability...Ch. 3 - Prob. 3.32STPECh. 3 - If the events E, F, G are independent. show that...Ch. 3 - Players 1,2,3, are in a contest. Two of them are...Ch. 3 - If 4 balls are randomly chosen from an urn...Ch. 3 - In a 4 player tournament, player 1 plays player 2,...Ch. 3 - In a tournament Involving players 1,..., n,...
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