STAT213 Worksheet #3

Seven people get on an elevator. They have 12 floors to choose from.

1) List the sample space for how the people can choose the floors. (There are 15 events.)

2) Compute the probability for each event in the sample space. (see key for solution)

3) If it known that 5 of the people are attending a meeting on the 10^th floor, what is the probability the remaining 2 people are choosing two other separate floors? (e.g. one person on the 2^nd floor, the other on the 9^th floor) (90.91%)

A Uno deck of cards has 12 faces (numbered 1 through 12) and 4 colours (I think!) for a total of 48 cards.

4) If you select six cards, list the sample space. (There are 9 events)

5) Compute the probability for each event in the sample space (see key for solution)

6) If you select 6 cards, what is the probability of having 2 threes or 4 red cards? (9.04%)

7) If you select 6 cards from the Uno deck and exactly two of the cards are sevens, what is the sample space? What is the probability of each event in the sample space? (see key for answer)

8) A train has 20 stations to choose from. There are 30 people on the train. What is the probability that 6 stations are each chosen by 3 people (18 in total), 3 stations are each chosen by 2 people (6 in total) and the rest of the people all choose different stations? (0.43%)

9) In class, we worked out the distribution for 4 letters/4 envelopes with X being the number of correct matches. We deduced that P(0) = 9/24 by taking advantage of the properties of a proper probability distribution. Show how else we could deduce this probability such as by how we deduced P(2) or P(1).

10) Work out the distribution for 5 letters/5 envelopes with X being the number of correct matches.

From the textbook:

Section 3-6

Q18 (page 159)

Q24 (page 160)

Q30 (page 160)

Q34 (page 161)

Q40 (page 162)