Please solve both questions and explain how Thanks A particu

Please solve both questions and explain how. Thanks!

A particular pitching machine is manufactured so that it will throw the ball into the strike zone of a 6-foot batter 90% of the time. What is the average number of pitches that it will throw in order to walk a batter (that is, throw 4 pitches outside of the strike zone)? what is the probability that the fourth ball will be thrown on the seventh pitch?

Solution

What is the average number of pitches that it will throw in order to walk a batter?

Probability of a ball to thrown out of strike zone = 1-0.9 = 0.1

Let X denote the number of pitches required to throw 4 pitches out of strike zone.

Let E denote the expected average number of pitches that it will take to throw in order to walk a batter.

E = 4*P(X=4)+5*P(X=5)+6*P(X=6)+.....

E=4*(0.1)⁴ +5*C(4,3)(0.1)⁴(0.9) +6*C(5,3)(0.1)⁴(0.9)²+....

E=40

Thus on an average it would take 40 pitches in order to walk a batter.

What is the probability that fourth ball will be thrown on the seventh pitch?

P(X=7) = C(6,3)(0.1)⁴(0.9)³

P(X=7) = 0.01