probability, day 1 answers warm-up · notes: example 1: a. b. 8 outcomes c. 1 path leads to hhh d....
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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
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