Bayesian Statistics: An Introduction, 4th Edition

1.6 Exercises on Chapter 1

1. A card came is played with 52 cards divided equally between four players, North, South, East and West, all arrangements being equally likely. Thirteen of the cards are referred to as trumps. If you know that North and South have ten trumps between them, what is the probability that all three remaining trumps are in the same hand? If it is known that the king of trumps is included among the other three, what is the probability that one player has the king and the other the remaining two trumps?

2.

a. Under what circumstances is an event A independent of itself?

b. By considering events concerned with independent tosses of a red die and a blue die, or otherwise. give examples of events A, B and C which are not independent, but nevertheless are such that every pair of them is independent.

c. By considering events concerned with three independent tosses of a coin and supposing that A and B both represent tossing a head on the first trial, give examples of events A, B and C which are such that although no pair of them is independent.

3. Whether certain mice are black or brown depends on a pair of genes, each of which is either or . If both members of the pair are alike, the mouse is said to be homozygous, and if they are different it is said to be heterozygous. The mouse is brown only it it is homozygous . The offspring of a pair of mice have two such ...