Chapter 11.9, Problem 16E

a.

To determine

To find the probability that the player will score on her next 2 attempts

Answer to Problem 16E

The probability of that the player will score a goal on her next two attempts is $\frac{289}{1000}$ .

Explanation of Solution

Given information:

A field hockey player scores a goal in 17% of her goal attempts.

Calculation:

Let P be the probability of the event that the player scores in the next 2 attempts.

The probability of scoring goal on her first attempt is $\frac{17}{100}$

  $\begin{array}{l}P\text{(goal on her next 2 attempts)}=\frac{17}{100}\times \frac{17}{100}\\ =\frac{289}{10000}\end{array}$

Hence,

The probability of that the player will score a goal on her next two attempts is $\frac{289}{1000}$ .

b.

To determine

To find the probability that the player will score in next 3 attempts

Answer to Problem 16E

The probabilitythat the player will score in next 3 attempts is $\frac{4913}{1000000}$

Explanation of Solution

Given information:

A field hockey player scores a goal in 17% of her goal attempts.

Calculation:

Let P be the probability of the event that the player scores in the next 2 attempts.

The probability of scoring goal on her first attempt is $\frac{17}{100}$

  $\begin{array}{l}P\text{(goal on her next 2 attempts)}=\frac{17}{100}\times \frac{17}{100}\\ =\frac{289}{10000}\end{array}$

Therefore,

  $\begin{array}{l}P\text{(scores in the next 3 attempts)}=\frac{17}{100}\times \frac{17}{100}\times \frac{17}{100}\\ =\frac{4913}{1000000}\end{array}$

The probabilitythat the player will score in next 3 attempts is $\frac{4913}{1000000}$

c.

To determine

To give reasons that each attempt is independent to previous one.

Answer to Problem 16E

It is reasonable to assume that each attempt is independent to previous one, as each game is a new game irrespective of the fact that this much goals were scored by the player in the previous match.

Explanation of Solution

Given information:

A field hockey player scores a goal in 17% of her goal attempts.

It is reasonable to assume that each attempt is independent to previous one , as each game is a new game irrespective of the fact that this much goals were scored by the player in the previous match.