×
×

# Each of three football players will attempt to kick a ISBN: 9780321923271 41

## Solution for problem 7E Chapter 1.4

Probability and Statistical Inference | 9th Edition

• Textbook Solutions
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants Probability and Statistical Inference | 9th Edition

4 5 1 246 Reviews
26
0
Problem 7E

PROBLEM 7E

Each of three football players will attempt to kick a field goal from the 25-yard line. Let Aidenote the event that the field goal is made by player i, i = 1, 2, 3. Assume that A1, A2, A3 are mutually independent and that P(A1) = 0.5, P(A2) = 0.7, P(A3) = 0.6.

(a) Compute the probability that exactly one player is successful.

(b) Compute the probability that exactly two players make a field goal (i.e., one misses).

Step-by-Step Solution:

Step 1 of 3 :

Given, each of three football players will attempt to kick a field goal from the 25-yard line.

Let denote the event that the field goal is made by player i , where i = 1, 2, 3.

We have to assume that , and are mutually independent

Where, P( ) = 0.5 , P( ) = 0.7 and P( ) = 0.6

Step 2 of 3 :

The claim is to find the probability that exactly one player is successful

P(exactly one player successful) = P( + P( +

P( Where , = 1 - = 1  - 0.5

= 0.5 = 1 - = 1  - 0.7

= 0.3

and = 1 - = 1  - 0.6

= 0.4

P(exactly one player successful) = (05 0.3 0.4)  + ( 0.5 0.7 0.4) +

( 0.5 0.3 0.6)

= 0.06  + 0.14 + 0.09

= 0.29

Therefore, the probability that exactly one player is successful is 0.29

Step 3 of 3

##### ISBN: 9780321923271

Unlock Textbook Solution