Question

During a basketball game, Courtney is shooting two free throws. She makes 90% of her free throws. Assumingthat her free throws are independent events, find the percent chance that she...a. is in the groove and makes both free throws. %b. makes the first and then misses the second. %c. misses the first and then makes the second.%d. struggles and misses both of her free throws. %e. What is the sum of these four answers? %

Answer 1

ANSWER:

a. 81%

b. 9%

c. 9%

d. 1%

e. 100%

STEP-BY-STEP EXPLANATION:

Because they are independent events, one event does not affect the other. Therefore, in each case it would be the product of each event.

Given:

Probability of scoring: 90%

Probability of not scoring: 10%

is in the groove and makes both free throws:

$p=0.90\cdot0.90=0.81\cdot100=81\%$

makes the first and then misses the second.

$p=0.90\cdot0.10=0.09\cdot100=9\%$

misses the first and then makes the second.

$p=0.10\cdot0.90=0.09\cdot100=9\%$

struggles and misses both of her free throws.

$p=0.10\cdot0.10=0.01\cdot100=1\%$

The sum of all these probabilities would be:

$\begin{gathered} P=81\%+9\%+9\%+1\% \\ P=100\% \end{gathered}$