Question

. a woman has n keys, of which one will open her door. (a) if she tries the keys at random, discarding those that do not work, what is the probability that she will open the door on her kth try?

Answer 1

The probability that the woman will open the door on her kth try is given by the formula:

P(k) = (1/n) * [(n-1)/n]^(k-1)

where P(k) is the probability of opening the door on the kth try, n is the total number of keys, and k is the specific try.

The first factor, (1/n), represents the probability of selecting the correct key on any given try. The second factor, [(n-1)/n]^(k-1), represents the probability of not selecting the correct key on each of the previous (k-1) tries.

For example, if the woman has 5 keys and she wants to know the probability of opening the door on her 3rd try, the formula would be:

P(3) = (1/5) * [(5-1)/5]^(3-1) = (1/5) * (4/5)^2 = 0.1024 or 10.24%

Therefore, the probability that the woman will open the door on her kth try decreases as k increases.