Four diners have ordered a platter of desserts. The platter holds 8 chocolate chip cookies and 4 slices of chocolate cheesecake. The waiter gives each diner a randomly selected dessert. Let Y = the number of slices of cheesecake left on the platter after the first serving. The distribution of Y is

Y
0
1
2
3
4
P(Y)
0.005
0.114
0.429
0.381
0.071

Find the probability that there's more than one slice left, but not all of them are left, i.e.,



Give your answer in decimal form using three decimal places,e.g., 0.123

1.024

0.810

To find the probability that there's more than one slice left, but not all of them are left, we need to find the sum of the probabilities for Y being 2 or 3.

P(Y = 2) = 0.429
P(Y = 3) = 0.381

The probability that Y is either 2 or 3 is the sum of these two probabilities:

P(Y > 1 and Y < 4) = P(Y = 2) + P(Y = 3) = 0.429 + 0.381 = 0.810

Therefore, the probability that there's more than one slice left, but not all of them are left, is 0.810.