Question

A coin is tossed three times. An outcome is represented by a string of the sort HTT (meaning heads on the first toss, followed by two tails). The 8 outcomes are listed below. Assume that each outcome has the same probability. Complete the following. Write your answers as fractions. (If necessary, consult a list of formulas.) (a) Check the outcomes for each of the three events below. Then, enter the probability of each event.

Answer 1

Note: Final answers are highlighted in colour.

a)

Table 1.1

	Outcomes	Probability
	HHH	HHT	HTH	HTT	THH	THT	TTH	TTT
Event A: The last toss is heads	Check		Check		Check		Check		4/8=1/2
Event B: At least one toss is tails		Check	Check	Check	Check	Check	Check	Check	7/8
Event A and B: The last toss is heads and at least one toss is tails			Check		Check		Check		3/8

b)

Table 1.2

	HHT	HTH	HTT	THH	THT	TTH	TTT	Probability
Event A: The last toss is heads		Check		Check		Check		3/7

c)

P(A and B)= 3/8 (From table 1.1)

P(B)=7/8 (From table 1.1)

P(A and B PB)
= $\frac{3/8}{7/8}$ = 3/7

P(A | B) = 3/7 (From table 1.2)

Therefore = P(A | B)= 3/7

P(A and B PB)