A runner is determined to run a mile in 4.8 minutes or less. for this runner, the probability of achieving this goal is 25%. the runner will keep practicing until he successfully runs a mile in 4.8 minutes or less. what is the probability that he will be successful for the first time on his fourth practice run?
a) 0.012
b) 0.105
c) 0.316
d)0.422
e) none of the above
The probability of success on any one practice run is 25%, or 0.25. The probability of failure is therefore 0.75.
The probability of not succeeding on the first three practice runs and then succeeding on the fourth is:
0.75 x 0.75 x 0.75 x 0.25 = 0.10547
Approximating to three decimal places, this gives us a probability of 0.105, so the answer is (b).