Question

A coin is tossed three times. An outcome is represented by a string of the sort HTT (meaning a head on the first toss, followed by two tails). The 8 outcomes are listed in the table below. Note that each outcome has the same probability. For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event. Event A: A tail on the first toss or the second toss (or both) Event B: A head on each of the first two tosses Event C: Two or more tails THH HTH HTT Outcomes HHT 0 TTH THT HHH 0 TTT Probability П 0 0 00 믐 X Españe

Answer 1

SOLUTIONS

For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event.

(a) Event A: A tail on the first toss or the second toss (or both)

`\frac{P(TXX)orP(XTX)orP(TTX)}{possible\text{ outcome}}`
`p(A\text{ tail on first or second or both\rparen=}(6)/(8)=(3)/(4)`

(b) Event B: A head on each of the first two tosses

`\frac{P(HHX)}{possible\text{ outcome}}=(2)/(8)=(1)/(4)`

(c) Event C: Two or more tails

`\frac{P(TTX)orP(XTT)orP(TXT)}{posible\text{ outcome}}`
`P(two\text{ or more tails\rparen=4/8=1/2}`