Question

During part of a recent season, pitcher Ubaldo Jimenez threw 2825 pitches. Of these, 1912 were fastballs, 228 were curve-balls, 457 were sliders, and the remaining were change-ups. Round all answers to 4 decimal places. a. What is the probability that Jimenez threw a fastball? b. What is the probability that Jimenez threw a curve-ball or a slider? C. What is the probability that the ball thrown was not a change-up?

Answer 1

The pitcher Ubaldo Jimenez threw 2825 pitches .  

That is , Total number of pitches thrown by Ubaldo is 2825 , n(S) = 2825

Number of fastballs = 1912 , n(fastballs) =1912

Number of curve-balls = 228 ,n(curve-balls)= 228

Number of sliders = 457 , n(sliders) = 457

Remaining Change-ups = Total numbers of pitches - ( n(fastballs) + n(curve-balls) +  n(sliders) )

=    2825 - ( 1912+228+457)

Remaining Change-ups  = 228

a) The probability of that Jimenez threw fastball is = $\frac{n(fastballs)}{n(Total pitches)}$

= 1912/2825 = 0.6768

The probability of that Jimenez threw a fastball is 0.6768  

b) Lets assume the  curve-ball and  slider is independant of each other

The probability of that Jimenez threw a curve-ball or slider is given by

p(curve-balls) = $\frac{n(curveballs)}{n(Total pitches)}$ , p (sliders) =  $\frac{n(sliders)}{n(Total pitches)}$

= $\frac{228}{2825}$ = $\frac{457}{2825}$

= 0.0807 = 0.1617

= p(curve-balls) + p(sliders) - p(curve-balls) *   p(sliders)

=    0.0807 + 0.1617 -     0.0807 *   0.1617

= 0.2424 - 0.01305

= 0.2293

The probability of that Jimenez threw a curve-ball or slider is    0.2293

c) The probability that the ball thrown was not a change-up is given by

p( change-up) =  $\frac{n( changeup) }{n( total pitches }$   

= 228/2825

= 0.0807

= 1 - p( change-up)

= 1 - 0.0807

= 0.9193   

The probability that the ball thrown was not a change-up is 0.9193