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.