Question

Problem:

Suppose that the probability of making a 3 pointer is p = 35%.

a) Calculate the probability that you make your third shot ON your fifth attempt.

b) Calculate the probability that you make your third shot BY your fifth attempt.

c) Calculate the expected value and variance for the NUMBER OF MISSES that you have prior to making your third shot.

d) Calculate the expected value for the TOTAL NUMBER OF SHOT ATTEMPTS that you take to make 3 shots.

Answers from the back of the textbook:

a) 0.1087

b) 0.2352

c) 5.571 and 15.92

d) 8.571

Answer 1

a)

P( third shot ON your fifth attempt ) =P(exactly 2 shot on first 4 attemt and 3rd shot on 5th)

=((₄C₂)*(0.35)²*(0.65)²)*0.35 =0.3105*0.35 =0.1087

b)

probability that you make your third shot BY your fifth attempt

=P(third shot on 3rd attemt)+P(3rd shot on 4th )+P(3rd on 5th)

=0.35³+((₃C₂)*(0.35)²*(0.65)¹)*0.35+((₄C₂)*(0.35)²*(0.65)²)*0.35

=0.0429+0.2389*0.35+0.1087 =0.2352

c)

expected value =r/p-r =3/0.35-r =5.571

varaince =σ2=r(1-p)/p2=3*(1-0.35)/0.35^2 =

15.92

d)

expected number =r/p=3/0.35 =8.571