Question 1
a)
A
restaurant serves 6 combos. If there is a party of 4 people, what is the sample
space? What is the probability of each event in the sample space? (see key)
b)
For
the party of 4 people, if at least 2 combos are chosen, what is the probability
that at least 3 combos are chosen?
(83.72%)
Question 2
A euchre deck
consist of 24 cards: 9,
10, jack, queen, king and ace of each suit. As with poker, each player receives
5 cards.
a)
Compute
the probability for each event in the sample space. (There are 6 events; see
key for solution)
b)
What is the
probability a euchre hand has 3 spades or 2 jacks? (22.19%)
c)
If a player has
exactly 2 jacks, what is the probability of each event in the sample
space? (There are 3 events; see key for
solution)
Question 3
A box has 12 balls: 4 white, 4 red and 4 blue. You draw
3 balls.
a)
Find the
probability of drawing one of each colour. (29.09%)
b)
Find the
probability of drawing at least 1 blue. (74.55%)
c)
If at least 1 of
the 3 balls chosen is red, what is the probability that you drew at least 2 red
balls? (31.71%)
Question 4
a)
A committee has
14 members. If it needs to fill the president, VP, secretary and treasurer
positions from among the 14, how many ways can the positions be
filled? (24,024)
b)
Suppose the
committee had to choose 3 people to go on a business trip. How many ways can
they choose the 3 people? (364)
c)
Suppose the
committee has 6 senior members and 8 junior members. If at least 1 of the 3
people going on the trip must be a senior member, how many ways can they be
chosen? (308)
Question 5
a)
Suppose a
4-digit alphanumeric password can be filled with either numbers or letters (not
case-sensitive). How many passwords can be created if none of the letters or
numbers can be repeated? (1,413,720)
b)
Same situation
as part a, but the first digit must be a letter. (1,021,020)