Chapter 13.10, Problem 23PPS

A

To determine

The professional basketball player makes a field goal $49\%$ of the time he shoots. Calculate the probability of the player that he will score on his next two attempts.

Answer to Problem 23PPS

P (Score in next 2 attempts) is $0.2401$

Explanation of Solution

Given:

Field goal: $49\%$

Calculation:

In the fraction form, the data is given that the probability of the professional basketball player that score in when he shoots is $49\%$ . So the probability of scoring the goals in his next 2 attempts in the fraction form is given as,

P (Score in the first attempt) = $\frac{49}{100}$

P (Score in the second attempt) = $\frac{49}{100}$

P (Score in next $2$ attempts) = P (First) * P (Second)

  = $\begin{array}{l}=\frac{49}{100}\times \frac{49}{100}\\ =\left(\frac{49.49}{100.100}\right)\\ =\frac{2401}{10000}=0.2401\end{array}$

Conclusion:

Hence, the P (Score in next $2$ attempts)is $0.2401$

B.

To determine

The professional basketball player makes a field goal $49\%$ of the time he shoots. Calculate the probability of the player that he will score on his next four attempts.

Answer to Problem 23PPS

P (Score in next $4$ attempts) = $0.05765$

Explanation of Solution

Given:

Field goal: $49\%$

Calculation:

In the provided data the time calculated to the goal is $49\%$ . The probability in the next $4$ attempts in the fraction form is given as,

P (Score in the first attempt) = $\frac{49}{100}$

P (Score in the second attempt) = $\frac{49}{100}$

P (Score in the third attempt) = $\frac{49}{100}$

P (Score in the fourth attempt) = $\frac{49}{100}$

P (Score in next $4$ attempts) = P (First) * P (Second)*P (Third) * P (Fourth)

  = $\begin{array}{l}=\frac{49}{100}\times \frac{49}{100}\times \frac{49}{100}\times \frac{49}{100}\\ =\left(\frac{\mathrm{49.49.49.49}}{\mathrm{100.100.100.100}}\right)\\ =\frac{5764801}{100000000}=0.05765\end{array}$

Conclusion:

P (Score in next $4$ attempts) = $0.05765$

C.

To determine

The professional basketball player makes a field goal $49\%$ of the time he shoots. Determine the event.

Answer to Problem 23PPS

The event is dependent event.

Explanation of Solution

Given:

Field goal: $49\%$

P (Score in next $2$ attempts) is $0.2401$

P (Score in next $4$ attempts) = $0.05765$

This is the dependent event as when two events are dependent then one event can influence the total probability of the other event that is second event. A dependent event is the event that relies on the other event to happen first.

Conclusion:

Hence, this is the dependent event.