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?
The probability the runner achieves their goal on the fourth try involves 3 failed attempts and 1 success. Therefore, the probability of this happening is the probability of failure (75%) raised to the power of the number of tries minus 1 (3), multiplied by the probability of success (25%).
P(success on the 4th try) = (0.75^3) * 0.25 = (0.421875) * 0.25 = 0.10546875
The probability that he will achieve this goal for the first time on his fourth practice run is approximately 10.55%.