MAT 126
Test 1
Name:
2.1 Explain what is meant by the probability of an event
1.
A coin is flipped some number of times and the result was 80% heads. Is it more
likely that the coin was flipped 10 times or 1000 times? Explain.
2.
Which of the following could represent a probability?
(a.)
(b.)
(c.)
(d.)
(e.)
3.
.0002
-.125
1.3
7
all of the above
Suppose you wanted to determine the probability that a buttered slice of toast
lands buttered side down. Explain how this question could be approached
empirically (experimentally) as well as theoretically.
2.2 Compute probabilities for events with equally likely outcomes
4.
In calculating the probability of rolling a sum of seven on a pair of dice, why is it
inappropriate to use the sample space S = { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 }?
5.
Use a table to represent a sample space for the experiment of rolling two six-sided
dice.
6.
Use your table in 5 to compute the following.
a.
P(rolling doubles)
b.
P(rolling a 7 or 11)
2.3 Compute probabilities of mutually exclusive events, complementary events, and the
union of events
7.
Suppose a card is drawn from a well-shuffled deck of 52 cards and the following
events:
A = the card is red
B = the card is a king
C = the card is a jack
D = the card is a heart
E = the card is a spade
Compute the following probabilities.
a.
P(A)
b.
P(B)
c.
P(not B)
d.
P(B or C)
e.
P(A and E)
f.
P(D or C)
g.
P(A and B)
h.
P(A or not A)
2.4 Use a tree diagram to compute probabilities
8.
9.
A coin is tossed and a die is rolled. What is the probability that . . .
a.
The coin lands “heads” and the die shows a six?
b.
the coin lands “heads” or the die shows a six?
Create a rug diagram or a tree diagram for the following “one-and-one” situation
in basketball. Liz has a 65% chance of making the 1st shot. If she makes the first
shot, she has a 70% chance of making the 2nd shot.
Calculate the probabilities
P( 0 points) =
P(1 point) =
P(2 points) =
2.9 Calculate expected value
10.
Calculate the expected number of points for Liz in a one-and-one situation above.
11.
A die is rolled. If the number rolled is odd, Player A wins $1 from Player B. If it
is a 6, A wins $4 from B. Otherwise B wins $2 from A.
Set up the table of payoffs and probabilities.
Compute the expected value for A’s winnings.
Is this a fair game? Explain.
2.8 Calculate conditional probabilities
12.
Consider the experiment of rolling a 6-sided die and the following events.
A = rolling an even number
B = rolling a six
C = rolling a number divisible by 3
Compute the following probabilities.
a.
P(B|A)
b.
P(A|B)
c.
P(B|C)
d.
P(A|B)
2.7 Use odds in favor and odds against an event to solve probability problems
13.
If the probability of winning a game is 7/9, what are the odds for winning?
2.5 Apply the fundamental counting property to calculate probabilities
14.
How many 3-digit numbers contain no 4’s? How many 3-digit numbers contain at
least one 4?
15.
How many ways can the letters in the word “COMPUTER” be arranged?
2.6 Use permutations and combinations to calculate probabilities
16.
A rock-climbing club has fifteen members. If the club wishes to form a committee
of four members, in how many ways can this committee be formed?
17.
In how many ways can 7 players be assigned to 5 different positions on a
basketball team?
18.
A lot of 25 television sets consists of 10 defective sets and 15 good ones. A
sample of 3 sets is chosen. Use combinations to calculate the following
probabilities:
a.
all defective sets
b.
2 defective sets