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Chapter 6 Awesomely Entertaining Probability Practice Test |
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1 |
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What is the probability of rolling a combined score greater than 4
with a
set of dice (2 cubes)?
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Score |
Probability |
Outcomes Making Up the Event |
| 2 |
(1/6)^2 * 1 = 1/36 |
1,1 |
| 3 |
(1/6)^2 * 2 = 2/36 |
1,2; 2,1 |
| 4 |
(1/6)^2 * 3 = 3/36 |
1,3; 3,1; 2,2 |
| Total |
1/6 |
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- (Prob. greater than 4) = 1 -
complement
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= 1 - 1/6
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= 5/6
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2 |
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What is the probability of getting at least two or more heads when tossing 3
coins?
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Score |
Probability |
Outcomes Making Up the Event |
| 2 |
(1/2)^3 * 3 = 3/8 |
HHT, HTH, THH |
| 3 |
(1/2)^3 * 1 = 1/8 |
HHH |
| Total |
1/2 |
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3 |
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What is the key assumption underlying all probability based predictions?
Law of Large Numbers |
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4 |
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The probability of event A is 10% and event B is 20%. The events are
disjointed. What is the intersection of the two events?
0 |
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5 |
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The probability of event A is 10% and event B is 20%. The events are
disjointed. What is the union of the two events?
30% |
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6 |
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If men wear red shoes 10% of the time while women wear red shoes 20% of the
time and there is a 55% probability that the next person walking by will be
male, what is the probability that a female will walk by wearing red shoes?
0.45 * 0.2 = 0.09 |
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7 |
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Refer to the question above. What percent of all people wearing red shoes
will be male? .055 |
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8 |
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If there is a 60 % chance that a person will be right, what is the
probability of all the people being wrong in a 5 person group?
(0.4)^5 = 0.0124 |
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9 |
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If 35 % of the people in the USA have brown hair, what is the probability of
finding a group of 5 people in which exactly one person has brown hair.
(0.65)^4 * 0.35 * 5 = 0.312 |
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10 |
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If 10 % of the people in the USA have green eyes and 20 % have blond hair,
what is the probability of finding a person with both green eyes and blond
hair? (assume green eyes and blond hair are independent)
0.1 * 0.2 = 0.02 |
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11 |
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If 20 % of the people in the USA have blue eyes and 70 % have brown hair,
what is the probability of finding a person with blue eyes or brown hair?
(assume blue eyes and brown hair are independent)
0.2 + 0.7 - (0.2 * 0.7) = 0.76 |
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12 |
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You flip a coin and get heads all 27 times in a row. Assuming that the coin
is fair, what is the probability of getting heads a 28th time.
0.5 |
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13 |
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Draw a graph of the
probability distribution for flipping 4 coins
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Score |
Probability |
Outcomes Making Up the Event |
| 0 |
(1/2)^4 * 1 =
1/16 |
HHHH |
| 1 |
(1/2)^4 * 4 =
4/16 |
HTTT, THTT, TTHT,
TTTH |
| 2 |
(1/2)^4 * 6 =
6/16 |
HHTT, HTHT, HTTH, THTH, THHT,
TTHH |
| 3 |
(1/2)^4 * 4 =
4/16 |
HHHT, THHH, HTHH, HHTH |
| 4 |
(1/2)^4 * 1 =
1/16 |
TTTT |
| Total |
16/16 |
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14 |
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The probability of getting an A in English is 20% and the probability of
getting an A in math is 40%. The probability of getting an A in both
classes is .04. are the 2 events independent?
- For independence: P(A and B)
= P(A) * P(B)
- P(A) * P(B) = 0.2 * 0.4
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= 0.08
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- Since 0.08 ≠ .04 getting an A in English is not
independent from getting an A in math
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15 |
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P(A) = 40%, P(B|A) = 20%, P(B) = 30% find P(A or B).
62% |