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).

Answer :

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) = (050.3 0.4) + ( 0.50.7 0.4) +

( 0.50.3 0.6)

= 0.06 + 0.14 + 0.09

= 0.29

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