AP Statistics – Unit 4 (Chapters 14-16) Extra Practice: Part 1

4.	If the individual outcomes of a phenomenon are uncertain, but there is nonetheless a regular distribution of outcomes in a large number of repetitions, we say the phenomenon is 	
A)	random               B) predictable              C) deterministic             D) none of the above	

5.	I toss a thumb tack 60 times and it lands point up on 35 of the tosses. The approximate probability of landing point up is 	
A)	35                B) 0.35               C) 0.58             D) 0.65	

8.	In a particular game, a fair die is tossed. If the number of spots showing is either 4 or 5 you win $1; if number of spots showing is 6 you win $4; and if the number of spots showing is 1, 2, or 3 you win nothing. If it costs you $1 to play the game, the probability that you win more than the cost of playing is 	
A)	0              B) 1/6                 C) 1/3                  D) 2/3	

10.	A game consists of drawing three cards at random from a deck of playing cards. You win $3 for each red card that is drawn. It costs $2 to play. For one play of this game, the sample space S for the net amount you win (after deducting the cost of play) is 	
A)	S = {$0, $1, $2, $3}        B) S = {$0, $3, $6, $9}       C) S = { –$2, $1, $4, $7}             D) S = { –$2, $3, $6, $9}	

If you draw an M&M candy at random from a bag of the candies, the candy you draw will have one of six colors. The probability of drawing each color depends on the proportion of each color among all candies made. Assume the table below gives the probability that a randomly chosen M&M has each color.
Color	Brown	Red	Yellow	Green	Orange	Tan	
Probability	.3	.3	?	.1	.1	.1 	

14.	If I select two M&Ms and the colors are independent, then the probability that both are the same color is 	
A)	0.01            B) 0.09             C) 0.22            D) 0.25	

15.	Event A occurs with probability 0.3. If event A and B are disjoint then 	
A)	P(B) £ 0.3              B) P(B) ³ 0.3             C) P(B) £ 0.7             D) P(B) ³ 0.7	

16.	Students at University X must be in one of the class ranks—freshman, sophomore, junior, or senior. At University X, 35% of the students are freshmen and 30% are sophomores. If a student is selected at random, the probability that her or she is either a junior or a senior is 	
A)	30%             B) 35%               C) 65%            D) 70%	

18.	I flip a coin twice and count the number of heads, which of the following is a valid probability model for the number of heads observed in two flips?	
A)	Number of Heads	
0	
1	
2	

Probability	
1/3	
1/3	
1/3	

B)	Number of Heads	
0	
1	
2	

Probability	
1/4	
1/4	
1/4	

C)	Number of Heads	
0	
1	
2	

Probability	
1/3	
1/2	
1/3	

D)	None of the above. 	

Ignoring twins and other multiple births, assume babies born at a hospital are independent events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5. 
22.	Referring to the information above, the probability that the next three babies are of the same sex is 	
A)	1.0              B) 0.125              C) 0.250                 D) 0.500	

23.	Referring to the information above, the probability that at least one of the next three babies is a boy is 	
A)	0.125             B) 0.333             C) 0.75                D) 0.875	

24.	Referring to the information above, the events       
A = the next two babies are boys          B = at least one of the next two babies is a boy          are 	
A)	disjoint               B) complements            C) independent            D) none of the above	

27.	In a certain town 60% of the households own a cellular phone, 40% own a pager, and 20% own both a cellular phone and a pager. The proportion of households that own a cellular phone but not a pager is 	
A)	20%           B) 30%             C) 40%            D) 50%	

34.	Event A occurs with probability 0.4. The conditional probability that A occurs given that B occurs is 0.5, while the conditional probability that A occurs given that B does not occur is 0.2. What is the conditional probability that B occurs given that A occurs? 	
A)	0                B) 4/7                C) 5/8              D) this cannot be determined from the information given	

35.	Event A occurs with probability 0.8. The conditional probability that event B occurs given that A occurs is 0.5. The probability that both A and B occur 	
A)	is 0.3           B) is 0.4           C) is 0.8            D) cannot be determined from the information given	

36.	Event A occurs with probability 0.3 and event B occurs with probability 0.4. If A and B are independent, we may conclude 	
A)	P(A and B) = 0.12            B) P(A|B) = 0.3              C) P(B|A) = 0.4             D) all of the above	

37.	A plumbing contractor puts in bids in on two large jobs. Let the event that the contractor wins the first contract be A and the event that the contractor wins the second contract be B. Which of the Venn diagrams on this and the next page has shaded the event that the contractor wins exactly one of the contracts? 	

	A)          B)       C)      D) 	

38.	The probability of a randomly selected adult having a rare disease for which a diagnostic test has been developed is 0.001. The diagnostic test is not perfect. The probability the test will be positive (indicating that the person has the disease) is 0.99 for a person with the disease and 0.02 for a person without the disease. The proportion of adults for which the test would be positive is 	
A)	0.00099                B) 0.01998               C) 0.02097              D) 0.02100	

  AP Statistics – Unit 4 (Chapters 14-16) Extra Practice: Part 2

Let the random variable X be a random number with the uniform density curve given.

3.	Referring to the information above, P(X = 0.25) is 	
A)	0.00              B) 0.25            C) 0.75           D) 1.00	

4.	Referring to the information above, P(X £ 0) has value 	
A)	0.0            B) 0.1             C) 0.5             D) 1.0	

5.	Referring to the information above, P(0.7 < X < 1.1) has value 	
A)	0.30           B) 0.40              C) 0.60              D) 0.70	

6.	Suppose there are three balls in a box. On one of the balls is the number 1, on another is the number 2, and on the third is the number 4. You select two balls at random and without replacement from the box and note the two numbers observed. The sample space S consists of the three equally likely outcomes {(1, 2), (1, 3), (2, 3)}. X, the total of the two balls selected, has probabilities 
	
X	
 3	
 4	
 5	

Probability	
1/3	
1/3	
1/3	

The probability that X is at least 4 is 	
A)	0               B) 1/3               C) 2/ 3             D) 1.0	

10.	A random variable is 	
A)	a hypothetical list of the possible outcomes of a random phenomenon	
B)	any phenomenon in which outcomes are equally likely	
C)	any number that changes in a predictable way in the long run	
D)	a variable whose value is a numerical outcome of a random phenomenon	

12.	The probability histogram for a random variable X corresponds to which of the following distributions for X?

A)	 X 	
0	
1	
2	
3	
4	

P(X)	
0.06	
0.25	
0.38	
0.25	
0.06	

B)	 X 	
0	
1	
2	
3	
4	

P(X)	
0.10	
0.25	
0.30	
0.20	
0.15 	

C)	 X 	
0	
1	
2	
3	
4	

P(X)	
0.10	
0.25	
0.30	
0.25	
0.10	

D)	None of the above	

Suppose there are three balls in a box. On one of the balls is the number 1, on another is the number 2, and on the third is the number 3. You select two balls at random and without replacement from the box and note the two numbers observed. The sample space S consists of the three equally likely outcomes {(1, 2), (1, 3), (2, 3)}. Let X be the total of the two balls selected. 
17.	Referring to the information above, the mean of X is 	
A)	2.0              B) 14/6              C) 4.0             D) 26/6	

18.	Referring to the information above, the variance of X is 	
A)	1/3             B) 2/3           C) 1             D) 4	

19.	In a particular game, a ball is randomly chosen from a box that contains three red balls, one green ball, and six blue balls. If a red ball is selected you win $2, if a green ball is selected you win $4, and if a blue ball is selected you win nothing. Let X be the amount that you win. The expected value of X is 	
A)	$1             B) $2               C) $3                D) $4	

26.	A random variable X has mean mX and standard deviation sX. Suppose n independent observations of X are taken and the average J of these n observations is computed. If n is very large, the law of large numbers implies 	
A)	that J will be close to mX                                                     B) that J will be approximately normally distributed	
C)	that the standard deviation of J will be close to sX             D) all of the above	

A psychologist studied the number of puzzles subjects were able to solve in a five-minute period while listening to soothing music. Let X be the number of puzzles completed successfully by a subject. The psychologist found that X had the following probability distribution.

Value of X	1	2	3	4	
Probability	0.2	0.4	0.3	0.1	

31.	Referring to the information above, the mean number of puzzles completed successfully, mX, is 	
A)	1               B) 2               C) 2.3            D) 2.5	

32.	Referring to the information above, if three subjects solve puzzles for five minutes each and the number of puzzles solved by each subject is independent of each other, then the mean of the total number of puzzles solved by the three subjects is 	
A)	2.3              B) 2.5               C) 6.9              D) 7.5	

33.	I roll a fair die and count the number of spots on the upward face. A fair die is one for which each of the outcomes 1, 2, 3, 4, 5, and 6 are equally likely. According to the law of large numbers 	
A)	several (four or five) consecutive rolls for which the outcome 1 is observed is impossible in the long run. If such an event did occur, it would mean the die is no longer fair	
B)	after rolling a 1, you will usually roll nearly all the numbers at least once before rolling a 1 again	
C)	in the long run, a 1 will be observed about every sixth roll and certainly at least once in every 8 or 9 rolls	
D)	none of the above is true	

The weight of medium-size tomatoes selected at random from a bin at the local supermarket is a normal random variable with mean m = 10 ounces and standard deviation s = 1 ounce. Suppose we pick two tomatoes at random from the bin, so the weights of the tomatoes are independent. 

37.	Referring to the information above, the difference in the weights of the two tomatoes selected (the weight of first tomato minus the weight of the second tomato) is a random variable with which distribution? 	
A)	N(0, 0.5)               B) N(0, 1.41)              C) N(0, 2)            D) uniform with mean 0	

38.	Referring to the information above, the probability that the difference in the weights of the two tomatoes exceeds 2 ounces is 	
A)	0.0170               B) 0.0340               C) 0.0680               D) 0.1587	

Answer Key (part 1)
4.A	5.C	8.B	10.C	14.C	15.C	16.B	18.A	22.C	23.D	24.D	27.C	34.C
35.B	36.D	37.C	38.C

Answer Key (part 2)
3.A	4.A	5.A	6.C	10.D	12.B	17.C	18.B	19.A	26.A	31.C	32.C
33.D	37.B	38.B