Worksheet on Probability

1) The colors of M & M's have the following probabilities of being
drawn from a bag.

0.2 - Brown 
0.1 - Red 
0.1 - Green 
0.1 - Orange 
0.3 - Blue 

a) If Yellow is the only color left, what is the probability of
drawing a yellow M & M?


b) What the probability of drawing either a brown or a red M & M?

2) How many different five-card poker hands can be drawn from a
52-card deck of cards?  Note that order is not important.

3) What is the probability of drawing a royal flush? 
(club A - club K - club Q - club J - club 10)
(note that these cards are just examples of one possible selection,
you will need to find all possible such combinations)


4) What is the probability of drawing a four-of-a-kind? 
(club 9 - heart 9 - spade 9 - diamond 9 - other)

5) What is the probability of drawing a full house? 
(club 5 - heart 5 - spade 5 - diamond 10 - heart 10)

6) What is the probability of drawing a three-of-a-kind? 
(club 6 - heart 6 - spade 6 - other - other)

7) What is the probability of drawing two pair? 
(club 3 - hearts 3 - spade 8 - diamond 8 - other)

8) Stanford U. received 16842 applications from prospective students.
Of these, 2596 were accepted.

a) What is the probability that a random applicant was accepted to
Stanford?

b) What is the probability that a random applicant was not accepted
to Stanford?


9) A test contains 15 true-false questions.  

a) Assuming no answers are left blank, how many ways can the test be
completed?


b) If you guess at every question, how many should you expect to get
correct? (might be a fraction)


c) If you guess at every question, what is the probability of
getting 15 correct? 14? 13? 13 or more?  (For 14 and 13, think of these
as choosing 14 correct answers from 15 possible.)