4. Three couples go out for ice-cream. They designate one person among the n-6 of them to

place the order for the 6 ice-creams. How many possible orders are there if the store offers

k3 different flavors (chocolate, vanilla and strawberry)? HINT: k-1 = 2 bars provide

k=3 spaces for the orders. e.g. (..) means 1 chocolate, 3 vanillas and 2 strawberries. Thus

arrangements of k-1 bars and n dots count all the possible orders.

(A) 42

(B) 40,320

(C) 7

(D) 56

(E) 28

5. Shuffle a standard deck of 52 cards and take the top 10 cards. What is the probability of

observing 3 cards with a number (i.e. 2,3,..., 10 in other words not a letter card A,J,Q,K)

?. Choose the closest.

(A) 1/1000

(B) 5/1000

(C) 1/10

(D) 5/100

(E) 1/100

6. You roll a fair die three times. Compute the probability that you roll at least one 5. The

closest answer is:

(A) 45%

(C) 58%

(D) 42%

(E) 48%

7. If three fair coins are tossed, what is the probability that all three faces will be the same?

(A) 15%

(B) 1/4

(C) 0.1

(D) 1/2

(E) 1/8

8. A box contains 100 balls of which 35 are red. Five balls are chosen at random from this box.

We want to compute the difference between the probabilities of getting exactly 3 red balls when

the sampling is done with replacement and without replacement. The closest answer for this

difference is

(A) -1%

(B) 1%

(C) -11%

(D) 11%

(E) 0%

9. You know that Mrs. Smith has two kids. If someone mentions that she saw Mrs. Smith boy

in the street; What's the probability that Mrs. Smith has two boys? (Assume equal apriori

probability for boys and girls).

(A) 1/4

(B) 2/3

(C) 1/2

(D) Not enough information given.

(E) 1/3