Question

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

Answer 1

Answer:

0.069793787 Approximately = 0.07

Step-by-step explanation:

From this question we have total number of keys to be 12,out of these 12, we know that only one key can open the office.

The probability that this 1 key can open the office is 1/12 = 0.083

Going further we have to apply the geometric distribution.

From the question the door opens after the 3rd time. So 2 trials have failed to open this door.

P(X=3) = (1-0.083)²(0.083)

= 0.840889x0.083

= 0.069793787

Approximately

0.07