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Theoretical and Experimental Probability Answers

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The table shows the results of a survey in which 10th-grade students were asked how many siblings (brothers and/or sisters) they have.

Question illustration
6
65%
7
70%
7
75%
8
80%
2
Free Preview

A briefcase has a three-digit lock code that does not include zero as a digit.What is the probability that the lock code consists of all even digits if the same digit is not used more than once in the lock code?

2
24 out of 504
6
60 out of 504
2
24 out of 84
6
60 out of 84
3

A rectangular board has an area of 648 square centimeters. The triangular part of the board has an area of 162 square centimeters. A dart is randomly thrown at the board.

Question illustration
1
18%
2
25%
3
35%
5
50%
4

Patty, Quinlan, and Rashad want to be club officers. The teacher who directs the club will place their names in a hat and choose two without looking. The student whose name is chosen first will be president and the student whose name is chosen second will be vice president.Which choice represents the sample space, S, for this event?

S
S = {PQR}
S
S = {PQR, PRQ, QPR, QRP, RPQ, RQP}
S
S = {PQ, PR, QR}
S
S = {PQ, QP, PR, RP, QR, RQ}
5

April is randomly choosing five CDs to bring in her car from the following: 6 pop CDs, 8 rock CDs, and 10 R&B CDs.What is the complement of April choosing five pop CDs?

c
choosing five CDs where none of them are pop
c
choosing five CDs where not all of them are pop
c
choosing five CDs where at least one of them is pop
c
choosing five CDs where all of them are pop
6

A padlock has a four-digit code that includes digits from 0 to 9, inclusive.What is the probability that the code does not consist of all odd digits if the same digit is not used more than once in the code?

A
120 out of 5,040
B
120 out of 3,024
C
2,904 out of 3,024
D
4,920 out of 5,040
7

Jasmine rolls a number cube 72 times. The number 2 is rolled 13 times and the number 3 is rolled nine times.To the nearest whole percent, what is the experimental probability of rolling a 2 or 3?

A
7%
B
18%
C
22%
D
31%
8

A cafeteria manager can choose from among six side dishes for the lunch menu: applesauce, broccoli, corn, dumplings, egg rolls, or French fries. He uses a computer program to randomly select three dishes for Monday’s lunch.What is the theoretical probability that applesauce and broccoli will both be offered on Monday?

A
10%
B
20%
C
50%
D
80%
9

A random number generator is used to create a list of 150 single-digit numbers. Of those 150 numbers, 72 are odd and 78 are even. The number 9 was generated 15 times.To the nearest whole percent, what is the experimental probability of an odd number other than 9 being generated?

A
38%
B
48%
C
52%
D
79%
10

Dayshawn can choose two of his four t-shirts to take on a weekend trip.If the t-shirts are labeled A, B, C, and D, which choice represents the sample space, S, for the event?

S
S = {ABCD}
S
S = {ABCD, DCBA}
S
S = {AB, AC, AD, BC, BD, CD}
S
S = {AB, BA, AC, CA, AD, DA, BC, CB, BD, DB, CD, DC}
11

A real estate map shows a 100-acre property:

A
0.30
B
0.70
C
0.40
D
0.60
12

Patty, Quinlan, and Rashad want to be club officers. The teacher who directs the club will place their names in a hat and choose two without looking. The student whose name is chosen first will be president and the student whose name is chosen second will be vice president.Which choice represents the sample space, S, for this event?

A
S = {PQR}
B
S = {PQR, PRQ, QPR, QRP, RPQ, RQP}
C
S = {PQ, PR, QR}
D
S = {PQ, QP, PR, RP, QR, RQ}
13

Five students, Adriana, Ben, Chandra, Diana, and Ernesto, would each like one of the four spots at the regional science fair. Their names are placed in a hat, and four names are chosen at random to decide who attends the fair.What is the theoretical probability that Chandra will be chosen as one of the science fair participants?

A
25%
B
60%
C
75%
D
80%
14

An insurance company predicts a 10% chance of an accident for drivers in a year. Out of 500 drivers, 65 report accidents.

A
It is equal to the theoretical probability.
B
It is greater than the theoretical probability.
C
It is less than the theoretical probability.
D
It cannot be determined.
15

Joe, Keitaro, and Luis play tennis. To decide who will play against each other in the first match, they put their names in a hat and choose two names without looking.What subset of the sample space, A, represents the complement of the event in which Joe plays in the first match?

A
A = {KL}
B
A = {KJ, KL}
C
A = {KL, LK}
D
A = {KJ, KL, LJ}
16

A cafeteria manager can choose from among six side dishes for the lunch menu: applesauce, broccoli, corn, dumplings, egg rolls, or French fries. He uses a computer program to randomly select three dishes for Monday’s lunch.What is the theoretical probability that applesauce and broccoli will both be offered on Monday?

A
10%
B
20%
C
50%
D
80%
17

A dartboard consists of a circle inscribed in a square. The area of the circle is square inches. The area of the square is 64 square inches.

Question illustration
A
22%
B
25%
C
75%
D
79%
18

The table shows the results of a survey in which 10th-grade students were asked how many siblings (brothers and/or sisters) they have.

Question illustration
A
65%
B
70%
C
75%
D
80%
19

A briefcase has a three-digit lock code that does not include zero as a digit.What is the probability that the lock code consists of all even digits if the same digit is not used more than once in the lock code?

A
24 out of 504
B
60 out of 504
C
24 out of 84
D
60 out of 84
20

A padlock has a four-digit code that includes digits from 0 to 9, inclusive.What is the probability that the code does not consist of all odd digits if the same digit is not used more than once in the code?

A
120 out of 5,040
B
120 out of 3,024
C
2,904 out of 3,024
D
4,920 out of 5,040

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