Question

Probability theory predicts that there is a 14% chance of a particular softball player hitting 2 home runs in a row. Which of these numbers of simulations of the softball player hitting balls would be most likely to produce results that are closest to those predicted by probability theory?
A.70
B.80
C.50
D.60

Answer 1

Probability of success is  p =0.14
Probability of failure is q = 1 - p = 0.86

From probability theory, the probability of two consecutive successes is
p^2 = 0.0196.

In a Bernoulli trial (with n simulations) and r successes), the probability of success is
nCr*p^r*q^(n-r).

Try n=70, r=2
P(success) = 70C2*0.14^2*0.86^68 = 0.0017

Try n=80, r=2
P(success) = 80C2*0.14^2*0.86^78 = 0.0005

Try n=50, r=2
P(success) = 50C2*0.14^2*0.86^48 = 0.0172

Try n=60, r=2
P(success) = 60C2*0.14^2*0.86^58 = 0.0055

The closest answer to 0.0196 occurs when = 50

Answer: C. 50