An absentminded professor does not remember which of his 12 keys will open his ocedoor. Suppose he tries them at random and with replacement. Find the probability that heopens his oce door after three tries.

Answer: 0.0052

Step-by-step explanation:

Total number of times experiment was performed (n) = 12

Probability of the event (that one key out of a total of 12 opens the door) = 1/12 = 0.083

Hence, p = 0.83

q = 1 - p = 11/12 = 0.917

x = 3

Since the experiment was performed n number of times, a binomial probability distribution can defined the experiment.

P (x=r) = nCr * p^r * q^n-r

P (x=3) = 12C3 * (0.083) ⁴ * (0.917) ^8

P (x=3) = 220 * (0.083) ⁴ * (0.917) ^8

P (x=3) = 0.0052