Exercise 7.1

Calculate the probability for each of the following:

a. Two tails in two tosses of a fair coin.

b. Three heads in three tosses of a fair coin.

c. Four heads in four tosses of an unfair coin where the probability of a head is 0.75.

d. Three sixes in three rolls of a fair die.

e. Five fours in five rolls of an unfair die where the probability of a four is 0.25.

Exercise 7.3

The Federal Bureau of Investigation trains sniffer dogs to find explosive material. At the end of the training, Lucy, the FBI's prize dog, is let loose in a field with four unmarked parcels, one of which contains Semtex explosives. The exercise is repeated three times, and on each occasion, Lucy successfully identifies the suspicious parcel.

a. What is the chance of an untrained dog performing such a feat? (Assume that the untrained dog would always approach one of the parcels at random.)

b. If there had been five parcels instead of four and the exercise had been carried out only twice instead of three times, would the chances of the untrained dog finding the single suspicious parcel have been greater or less?