Question

3. The Round Rock Express has a pitcher with an impressive winning record. Opposing teams are attempting to analyze his pitches. The pitcher throws a strike 35of the time. If the pitcher throws a strike the next pitch is a fastbal 40% of the time. If the pitcher doesn't throw a strike the next pitch is a fastball 80% of the time.

Answer 1

0.66

Explanation:

Given:

Let P(Throwing strike) = 0.35

So,

P(S') = 1 - 0.35 = 0.65

P(A / B) = P(A and B) / P(B)

P(Throwing fastball and thrown strike) = P(F / S) = 40% = 0.4

P(Throwing fastball not thrown strike) = P(F / S') = 80%

P(Throwing fastball not thrown strike) =0.8

So,

P(F and S) = 0.8 x 0.65

P(F and S) = 0.52

P(F) = [P(F / S) x P(S)] + [P(F / S') x P(S')]

= (0.4 x 0.35) + (0.8 x 0.65)

= 0.14 + 0.52

= 0.66