DS280 - Intro to Statistics

Lecture Review #6 - Combinatorial Probability

OBJECTIVES:

After today's class you should:

• be familiar with "factorial" notation (n!).
• understand mathematical "combinations" and be able to compute the number of combinations in a given situation.
• be able to use these in solving probability problems.

COMPUTATIONAL EXERCISES:

1) In the New Jersey State Lottery, bettors select 6 of 44 numbers. What's your chance of winning the grand prize (getting all 6 numbers right) on a given ticket?

2) In bridge (the card game), a deck of 52 cards is dealt out among four players (each receiving 13 cards).

a) How many different 13-card bridge hands are possible?

b) What's the probability that you're dealt 13 cards of the same suit?

c) What's the probability that all four players are dealt 13 cards of the same suits? [Hint: do it one player at a time. Once the first player has 13 spades (say), that affects the chances for the second player.]

SOLUTIONS:
1) 1 chance in 7,059,052
2a) 635,013,559,600
2b) 4/635,013,559,600
2c) (4/635,013,559,600)*(3/8,122,425,444)*(2/10,400,600),
       roughly one chance in 2,235,197,400,000,000,000,000,000,000
SEE DETAILED SOLUTIONS