Question

Consider the experiment of tossing a fair coin 3 times. For each coin, the possible outcomes are heads or tails.(a) List the equally likely events of the sample space for the three tosses.(b) What is the probability that all three coins come up heads? Notice that the complement of the event "3 heads" is "at least one tail." Use this information to compute the probability that there will be at least one tail.

Answer 1

Answer:

a)

H - H - H

H - H - T

H - T - H

H - T - T

T - H - H

T - H - T

T - T - H

T - T - T

b)

0.125 = 12.5% probability that all three coins come up heads.

0.875 = 87.5% probability that there will be at least one tail.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Question a:

Considering H for heads, T for tails:

H - H - H

H - H - T

H - T - H

H - T - T

T - H - H

T - H - T

T - T - H

T - T - T

(b) What is the probability that all three coins come up heads?

One outcome(H - H - H) out of 8, so:

$p = \frac{1}{8} = 0.125$

0.125 = 12.5% probability that all three coins come up heads.

Notice that the complement of the event "3 heads" is "at least one tail." Use this information to compute the probability that there will be at least one tail.

Sum of these probabilities is 100%, so:

1 - 0.125 = 0.875

0.875 = 87.5% probability that there will be at least one tail.