Question

1. Walt Disney world collects data regarding the guests in the park on a particular day: 17% of the guests are annual pass holders. - of those who are annual pass holders,63% are staying at Disney resort. - of those who are NOT annual pass holders, 28% are staying at a Disney resort.

a. If a guest is selected at random, what is the probability that the guest is an annual pass holder who is staying at a Disney resort?

b. If a guest is selected at random, what is the probability that the guest is NOT an annual pass holder and NOT staying at a Disney resort?

c. If a guest is selected at random, what is the probability that the guest is NOT staying at the Disney Resort?

2. A television network executive has a list of 7 sitcoms and 5 reality shows to schedule

a. The executive wants to select one show from the lists to feature in the primetime for each weekend evening, Friday-Sunday. How many different possible arrangements of the shows are there?

b. The executive wants to select 4 shows from the list to cut from the network's lineup. How many options does the executive have for a group of 4 shows to cut?

c. If the executive randomly selects 4 shows, what is the probability that he will choose 2 reality shows and sitcoms?

d. If the executive randomly selects 4 shows, what is the probability that at least one of them will be a reality show?

Answer 1

	Disney	Not Disney	Total
Annual Pass holder	10.71%	6.29%	17.00%
Not Annual Pass holder	23.24%	59.76%	83.00%
Total	33.95%	66.05%	100.00%

1)

Let total guest = X

a) Guest at annual pass holder = 17% of x = 0.17*x

Guest at annual pass holder with Disney = 0.63 * 0.17*x = 0.1071 x

Probability = 0.1071 * x/ x = 0.1071

b)

Guest at not annual pass holder = x - 17% of x = 0.83*x

Guest at not annual pass holder with not Disney = (1 -0.28) * 0.83*x = 0.5976 x

Probability = 0.5976* x/ x = 0.5976

c)

Guest at annual pass holder and not at disney = 0.17 * (1-0.63) = 0.0629
Guest at not annual pass holder and not at disney = 0.83 * (1-0.28) = 0.5976

Total = 0.0629 + 0.5976 = 0.6605

thanks

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