A box contains five keys, only one of which will open a lock. Keys are randomly selected and tried, one at a time, until

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A box contains five keys, only one of which will open a lock.
Keys are randomly selected and tried, one at a time, until the lock
is opened, without replacement.
Let Y be the number of the trial on which the lock is opened.

a. Find p(y), the probability mass function for Y.
b. Find F(y), the cumulative distribution function for Y.
c. Find P(Y < 3), P(Y ≤ 3) and P(Y=3) using the probability mass
function of Y that is derived in part (a).
d. If Y is a continuous random variable, we argued that, for all -∞
< a < ∞, P(Y=a)=0. Do any of your answers in part (c)
contradict this claim? Why or why not?
e. Find P (Y < 3), P (Y ≤ 3) and P(Y=3) using the cumulative
distribution function of Y that is derived in part (b).