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 Soutcomes 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: No tails on the first two tosses Event B: A head on each of the first two Event C: Alternating tall and head (with either coming first) O HTH P Outcomes EO THE Probability 0 0 0

Answer 1

ANSWER

EXPLANATION

For each event, there are 8 possible outcomes.

• In event A we know that there are no tails on the first two tosses, so we have either HHH or HHT.

• In event B there is a head on each of the first two tosses, so we have either HHH or HHT.

,

• In event C, heads and tails are alternating, so we have HTH or THT.

Note that for all events, only 2 of the 8 possible outcomes are favorable, so, for all, the probability is,

$P(event)=\frac{favorable\text{ }outcomes}{possible\text{ }outcomes}=\frac{2}{8}=\frac{1}{4}$

Hence, the probability for each of the three events is the same, 1/4.