)
1 What is the probability of rolling a combined score greater than 4 with a set of dice (2 cubes)?
2
3
(1/6)^2 * 1 =
1/36
(1/6)^2 * 2 =
2/36
1,1
1,2; 2,1
4
(1/6)^2 * 3 =
3/36
1,3; 3,1; 2,2
Total 1/6
(Prob. greater than 4) = 1 - complement
= 1 - 1/6
= 5/6
2 ) What is the probability of getting at least two or more heads when tossing 3 coins?
2 (1/2)^3 * 3 = 3/8 HHT, HTH, THH
3 (1/2)^3 * 1 = 1/8 HHH
Total 1/2
3 ) What is the key assumption underlying all probability based predictions?
Law of Large Numbers
4 ) 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
5 ) 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%
6 ) 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
7 ) Refer to the question above. What percent of all people wearing red shoes will be male? 38%
8 ) 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 = 0.01024
9 ) 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

10 ) 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
11 ) 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
12 ) 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
13 ) Draw a graph of the probability distribution for flipping 4 coins
13 )
Score Probability Outcomes Making Up the Event
0 (1/2)^4 * 1 = 1/16 TTTT
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 HHHH
Total 16/16

14 ) 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
= 0.08
Since 0.08 ≠ .04 getting an A in English is not independent from getting an A in math
15 ) P(A) = 40%, P(B|A) = 20%, P(B) = 30% find P(A or B). 0.4 + 0.2 - 0.4(0.2) = 0.62 or 62%
16 ) P(A) = 40%, P(B|A) = 20%, P(B) = 30% find P(A and B). 0.40(0.20) = 0.08 or 8%
17 ) P(A) = 40%, P(B) = 30%, for independent events, find P(A or B) 0.40 + 0.30 -
0.40(0.30) = 0.58 or 58%
18 ) P(A) = 40%, P(B) = 30%, for independent events, find P(A and B) 0.40(0.30) = 0.12 or 12%
19 ) P(A) = 40%, P(B) = 30%, for disjointed events, find P(A or B) 0.40 + 0.30 = 0.70 or 70%
20 ) P(A) = 40%, P(B) = 30%, for disjointed events, find P(A and B) 0%
21 ) How many possible outcomes are possible when rolling a pair of dice? 36
22 ) What is the probability of getting 7 when rolling a pair of dice? 1/6
23 ) Are disjointed events independent? NO!
24 ) 20% of the people read newspaper A, 30% read newspaper B. 10% read both newspapers. What % read no newspapers? Are reading newspaper A and B independent events? 40%
25 ) If an individual has a 60% chance of arriving at the correct verdict, what is the probability that no one on a jury will arrive at the correct verdict?
0.4^12 = 1.68 x 10 -5

26 ) Given the tree diagrams at left, determine if P(A) and
P(B) are disjointed, independent or conditional for each tree.
A) ___ Disjointed __________________________
B) ___ Conditional _________________________
C) __ Independent ________________________
27 ) The sheriff wants to set up random road blocks, stop each car and give each driver a breathalizer test to see if he or she is intoxicated. If a person is drunk, the test is 99% accurate but if a person is sober, the test is 98% accurate. 1% of all drivers are legally drunk. Of the individuals identified by the test as drunk, what % are actually sober?
Offer your analysis to the sheriff along with recommendations for how he should proceed. What is the probability of getting an inaccurate test?
Draw a tree diagram to obtain the following:
( Of individuals identified by the test as drunk, % actually sober )
=
=
[ 0.0198 / ( 0.0198 + 0.0099 ) ] x 100%
66.7%
( probability of inaccurate test )
= (0.0198 + 0.0001 ) x 100%
1.99%
Advice: test only for cause in order to avoid prosecuting a high % of innocent people.