Suppose there is a snack machine in the library which seems
to randomly malfunction. After you put money in it and select
a snack, it sometimes gives you the snack you asked for,
sometimes you get a snack you didn't ask for and just as often,
it gives you nothing. When you are in the library for a few
hours, you often end up wanting two snacks while you are there.
(a) State the sample space
Let Y = "You get the snack you want.
Let N = "You get a snack, but not the one you wanted.
Let 0 = "You get no snack at all".
Sample space = {YY, YN, Y0, NY, NN, N0, 0Y, 0N, 00}
(b) Find the probability of getting no snack both times.
P(00) = 1 way out of 8 = 1/8
(c) Find the probability of getting no snack at least once.
P(Y0 or N0 or 0Y or 0N or 00) = P(Y0)+P(N0)+P(0Y)+P(0N)+P(00) =
1/8+1/8+1/8+1/8+1/8 = 5/8
(d) Find the probability of not getting no snack both times.
That's a double negative, bad grammar.
You would get a snack both times.
1 - P(00) = 1 - 1/8 = 7/8
Edwin