Probability, Day 1 ANSWERS

Warm-up:

1. 14 2. 3/14 or 21.4% 3. 3/7 or 42.9% 4. 5/14 or 35.7% 5. Lemon

6. Cherry 7. Lemon 8. 4/7 or 57.1% 9. Grape 10. Grape

Notes:

Example 1: 1/9 or 11.1%

Example 2: 1/36 or 2.8%

Example 3: 1/4 or 25%

Classwork:

Problem 1 a. Not likely to happen b. Likely to happen c. Impossible d. Certain

Problem 2 a. Not likely to happen b. Likely to happen c. Not likely to happen d. Likely to happen

Problem 3 Yes.

1 5(6) (6') 1

6 6P P

and

2 4

(1 2) (1 2) ' 16 6

P or P or

Homework:

Problem 1 a. 1/2 b. 3/5 c. 2/5

Problem 2 a. 5/18 b. 7; 1/6 c. ½

Problem 3 a. 1/2 b. 2/13 c. 1/26

Problem 4 a. 31/120 b. 11/24 c. 5/6

Answers to Probability Day 2

Warm-up:

1. Card A – They have more numbers on their card that have the higher probabilities of being chosen than the

other two cards do.

2. Student choice. Answers may vary.

3. No – As long as other cards contain numbers that are possible, there is still a chance that their numbers would

be chosen.

Notes:

Example 1:

a. 83/130

b. 17/130

c. 15/26

d. 55/72

e. 30/47

Example 2:

Example 1 is an example of experimental probability because we collected results (we didn’t make

predictions).

Classwork:

Problem #1 Problem #2 Problem #3 Problem #4 a. 11/24 b. 5/12 c. 6/13 d. ½

a. 33 b. 15/67 c. 51.4% d. 73

a. 5/41 b. 22/41 c. 12/19

a. 22.7% b. 56.2% c. 62/81 d. 81/143

Homework:

Problem #1 Problem #2 Problem #3 a. P(B) = 2/5

P(W) = 7/15 P(R) = 2/15

b. Theoretical – expectation, no experiment conducted

a. 349/712 b. 477/1424 c. 76/145 d. 263/726 e. Experimental – data was

collected

a. 1/6 b. 97.5% c. 31/36

Problem #4 Problem #5 (for 5c and 5d, safely assume that there is no distinction between the two dice, and simply subtract the smaller number from the larger, in other words, positive differences only)

a. Experimental – data was collected to make this prediction

b. Theoretical – expectation based on a statement

c. Experimental – data was collected to make this prediction

a. 1/9 b. 5/36 c. 5/18 d. 13/36 e. 5/18

Answers to Probability Day 3

Notes:

Example 1:

a. b. 8 outcomes c. 1 path leads to HHH d. P(HHH) = 0.125 (or 1/8) e. 3 paths have two heads and one tail; P( two H

and one T) = 3(1/8) = 3/8 (04 0.375)

Example 2:

a. b. 6 paths total c. 2 paths lead to a red marble

Example 3:

a. Assuming equal likelihood of getting either toy…

b. Assuming equal likelihood of getting any of the three toys…

Example 4:

a. 10 outcomes b. (H, A) or (T, A) c. 2/10-1/5 or 0.20 d. 1/10 or 0.10 e. No. P(section A) = 1/3, P(H, A) = 1/6.

Homework:

1.

2.

a. 1/12 b. ¼ c. 5/12 d. 0

3.

a. 1/16

b. 1/169

c. 1/4

d. 1/169

4.

a. 0.03

b. 0.315

c. 0.45

5. (this one is a bit strange…)

a. 0.68

b. = f = 0.3608

c.

d.

e. = g = 0.9744

6. 12 different meals

7. 16 possible outcomes

Answers to Probability Day 4

Warmup:

1.

a. 13/47 = 0.277

b. 25/41 = 0.61

c. 2/11 = 0.182

2. 5/6

3. Theoretical – what we expect (do not conduct an experiment); Experimental – what

actually happens (after collecting data from an experiment)

Notes: Example 1:

a. 11/30 = 0.367 b. 19/30 = 0.633

Example 2: a. 0.03 b. 0.45

Example 3: a. 0.68 b. = f = 0.3608 c. d. e. = g = 0.9744

Example 4: 0.48 Example 5: 0.12

Homework: 1. 0.28; 0.24 2. 0.1774; 0.9582; 0.8644 3. ¼; 1/16; 5/8; ¾ 4. 0.425 5. 0.3; 0.1; 0.6 6. 11/850 = 0.013 7. 20/49 = 0.408; 5/7 = .714