Chapter 11.9, Problem 18E

a.

To determine

To find the probability that the player will score in next 2 attempts

Answer to Problem 18E

The probability of that the player will score a goal in next two attempts is $\frac{289}{100}$ .

Explanation of Solution

  $\begin{array}{l}\text{Let P be the probability of the event that the player scores in the next 2 attempts,}\\ \text{P(scores in the next 2 attempts)=}\frac{17}{100}\times \frac{17}{100}\\ =\frac{289}{10000}\end{array}$

b.

To determine

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

Answer to Problem 18E

The probability is $\frac{4913}{1000000}$

Explanation of Solution

  $\begin{array}{l}\text{Let P be the probability of the event that the player scores in the next 3 attempts,}\\ \text{P(scores in the next 3 attempts)=}\frac{17}{100}\times \frac{17}{100}\times \frac{17}{100}\\ =\frac{4913}{1000000}\end{array}$

c.

To determine

To find the general rule for a probability that a coin shows heads each time when it is tossed n times in a row

Answer to Problem 18E

The general rule is $\frac{1}{2^n}$

Explanation of Solution

  $\begin{array}{l}\text{n = 1 P(H)=}\frac{1}{2}\\ \text{n = 2 P(HH)=}\frac{1}{4}\\ \text{n =3 P(HHH)=}\frac{1}{8}\\ \Rightarrow \text{ P (H) = }\frac{1}{2^n}\end{array}$