Question

2. A golfer will play two holes of a course. Suppose that on each hole the player will score 3, 4, 5, 6, or 7, with these five scores being equally likely. Find the probability,
and explain how the answer was determined that the player’s total score for the two holes will be
a. 14.
b. 12.

Answer 1

Answer:

The probability that the player’s total score for the two holes will be  14 is 0.04

The probability that the player’s total score for the two holes will be  12 is 0.12

Step-by-step explanation:

Consider the provided information.

Each hole the player will score 3, 4, 5, 6, or 7, with these five scores being equally likely.

A) 14

It is given that the player’s total score for the two holes will be 14.

There is only one possible case to get a total score of 14.

If the player scores 7 on each hole, which is P(7)× P(7).

$P(7) = \frac{1}{5}$

Thus, the required probability is:

$P(Total:14)=P(7)\times P(7)$

$P(Total:14)=\frac{1}{5}\times \frac{1}{5}=0.04$

Hence, the probability that the player’s total score for the two holes will be  14 is 0.04

B) 12

It is given that the player’s total score for the two holes will be 12.

There are three ways to have a total score of 12.

7+5 = 12, 6+6 = 12, 5+7 = 12

$P(5)=P(6)=P(7)=\frac{1}{2}$

Thus, the required probability is:

$P(Total:12)=P(7)\times P(5)+P(6)\times P(6)+P(5)\times P(7)$

$P(Total:12)=\frac{1}{5}\times \frac{1}{5}+\frac{1}{5}\times \frac{1}{5}+\frac{1}{5}\times \frac{1}{5}=0.12$

Hence, the probability that the player’s total score for the two holes will be  12 is 0.12