Theoretical Probability Answer Key
Pages 273-275
1.
a. The list of possible outcomes is G, G, Y, Y, Y, Y, B (7 possible outcomes)
b. The theoretical probability of a:
i. Green tile is 2 out of 7 ( ). She can pull out 2 different green tiles.
ii. Yellow tile is 4 out of 7 ( ). She can pull out 4 different yellow tiles.
iii. Blue tile is 1 out of 7 ( ). She can only pull out 1 blue tile.
2. The theoretical probability that a girl will present 1st is 13 out of 30 ( ). This is because there are
30 students (see work below) in the class which means there are 30 names in the bag. Since any
girl can be draw there are 13 girls names in the bag that could be picked.
17(boys) + 13(girls) = 30(students)
3.
a. The list of possible outcomes is White, Yellow, Red, Black (4 possible outcomes)
b. The theoretical probability of the:
i. Spinner landing on black is 1 out of 4 ( ). It can only land on black.
ii. Spinner landing on red is 1 out of 4 ( ). It can only land on red.
iii. Spinner landing on yellow or white is 2 out of 4 ( ). It can land on yellow or
white.
Note* this can be reduced to 1 out of 2 ( )
iv. Spinner landing on not landing on yellow is 3 out of 4 ( ). It can land on black,
red, or white.
4.
a. The list of possible outcomes is 1, 2, 3, 4, 5, and 6. (6 possible outcomes)
b. The probability of a rolling a 1 is 1 out of 6 ( ). Shen can only roll a 1.
The probability of a rolling an even number is 3 out of 6 ( ). Shen can roll a 2, 4, or 6.
Note* this can be reduced to 1 out of 2 ( )
The probability of a rolling a number greater than 4 is 2 out of 6 ( ). Shen can roll a 5 or
a 6.
Note* this can be reduced to 1 out of 3 ( )
5.
a. The list of possible outcomes is B, B, B, B, B, B, B, B, B, R, R, R, R, R, R, R, R, R, R, R, R, R,
R, R, R, R, R, R, R, R, R, O, O, O, O, O, O, O, O, O, O, O, O, O, O, O, O, O, O, O, O, O, O, O,
O, O, O, G, G, G, G, G, G, G, G, G, G, G, G, G. (B=Black, R=Red, O=Orange, G=Green).
There are 70 possible outcomes.
b. The theoretical probability of the:
i. Picking a black marble is 9 out of 70 ( ). There are 9 different black marbles
that can be picked.
ii. Picking a green marble is 13 out of 70 ( ). There are 13 different black marbles
that can be picked.
iii. Picking a red or an orange marble is 48 out of 70 ( ). There are 22 different red
marbles and 26 different orange marbles (22+26=48) that can be picked.
Note* this can be reduced to 24 out of 35 ( )
6.
a. The probability of choosing a vowel is 2 out of 5 ( ), a U or an O can be picked. (YUKON)
b. The probability of choosing a vowel is 4 out of 12 ( ), an A or an E can be picked.
(SASKATCHEWAN)
Note* this can be reduced to 1 out of 3 ( )
c. The probability of choosing a vowel is 3 out of 7 ( ), an A, or a U can be picked.
(NUNAVUT)
d. The probability of choosing a vowel is 4 out of 8 ( ), an O, an I, or an A can be picked.
(MANITOBA)
Note* this can be reduced to 1 out of 2 ( )
7.
a. The list of possible outcomes is 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10. There are 10 possible
outcomes.
b. The probability of Shannon rolling an odd number is 5 out of 10 ( ). She can pick a 1, 3,
5, 7, or 9.
Note* this can be reduced to 1 out of 2 ( )
c. There is a 1 out of 5 ( ) chance of getting the digit 1. There are 2 ways that the digit 1
can be rolled, a 1 or a 10. This is a probability of 2 out of 10 ( ). This can be reduced to
1 out of 5 ( ) by dividing 2 and 10 by 2.
8. I would choose the 2nd spinner because I would have a greater chance to win. I will show the
probabilities of each spinner to prove this.
Spinner 1
Number of favorable outcomes = 2 (the stars)
Number of possible outcomes = 8 (8 wedges in the spinner)
Probability of getting a star =
Probability of not getting a star =
Spinner 2
Number of favorable outcomes = 2 (The Happy Face)
Number of possible outcomes = 5 (5 wedges in the spinner)
Probability of getting a happy face =
Probability of not getting a star =
Based on this information there is a higher probability of getting a happy face than a star
because while there are the same number of favorable outcomes there is fewer possible
outcomes on the second spinner.
9. Important information: There are 30 students in the class (2+4+3+1+5+3+2+3+3+1+1+2=30).
a. The probability of a March birthday is 3 out of 30( ).
Note* this can be reduced to 1 out of 3 ( )
b. The probability of a March birthday is 1 out of 30( ).
c. The probability of a birthday in June, July, or August is 8 out of 30( ).
Note* this can be reduced to 4 out of 15 ( )
d. The probability of a student not having a birthday in December is 28 out of 30( ).
Note* this can be reduced to 14 out of 15 ( )
10.
a.
b.