Mr. Rogers  AP Statistics Objectives

Chapter 6 Awesomely Entertaining Probability Practice Test  
1  ) 
What is the probability of rolling a combined score greater than 4
with a
set of dice (2 cubes)?


2  ) 
What is the probability of getting at least two or more heads when tossing 3
coins?


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  ) 


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) 

15  )  P(A) = 40%, P(BA) = 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(BA) = 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? = 1  40% or 60%  
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:
Advice: test only for cause in order to avoid prosecuting a high % of innocent people.

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