AP Statistics - Chapter 4A Warm-Ups

1. / I toss a penny and observe whether it lands heads up or tails up. Suppose the penny is fair, that is, the probability of heads is ½ and the probability of tails is ½. This means
A) / that every occurrence of a head must be balanced by a tail in one of the next two or three tosses
B) / that if I flip the coin many, many times, the proportion of heads will be approximately ½, and this proportion will tend to get closer and closer to ½ as the number of tosses increases
C) / that regardless of the number of flips, half will be heads and half tails
D) / all of the above
2. / A phenomenon is observed many, many times under identical conditions. The proportion of times a particular event A occurs is recorded. This proportion represents
A) / the probability of the event A B) the distribution of the event A
C) / the correlation of the event A D) the variance of the event A
6. / Suppose we have a loaded die that gives the outcomes 1–6 according to the following probability distribution:
X / 1 / 2 / 3 / 4 / 5 / 6
P(X) / 0.1 / 0.2 / 0.3 / 0.2 / 0.1 / 0.1
Note that for this die all outcomes are not equally likely, as they would be if the die were fair. If this die is rolled 6000 times, the number of times we get a 2 or a 3 should be about
A) / 1000 B) 2000 C) 3000 D) 4000
7. / Suppose we roll a red die and a green die. Let A be the event that the number of spots showing on the red die is 3 or less and B be the event that the number of spots showing on the green die is more than 3. The events A and B are
A) / disjoint B) complements C) independent D) reciprocals
9. / I select two cards from a deck of 52 cards and observe the color of each (26 cards in the deck are red and 26 are black). Which of the following is an appropriate sample space S for the possible outcomes?
A) / S = {red, black}
B) / S = {(red, red), (red, black), (black, red), (black, black)}, where, for example, (red, red) stands for the event “the first card is red and the second card is red”
C) / S = {0, 1, 2}
D) / All of the above

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
11. / The probability of drawing a yellow candy is
A) / .1 B) .2 C) .3 D) impossible to determine from the information given
12. / The probability that I do not draw a red candy is
A) / .1 B) .3 C) .7 D) .9
13. / The probability that I draw neither a brown nor a green candy is
A) / .1 B) .3 C) .4 D) .6
17. / Event A occurs with probability 0.2. Event B occurs with probability 0.8. If A and B are disjoint (mutually exclusive) then
A) / P(A and B) = 0.16 B) P(A or B) = 1.0 C) P(A and B) = 1.0 D) P(A or B) = 0.16
19. / Suppose there are three cards in a deck, one marked with a 1, one marked with a 2, and one marked with a 5. You draw two cards at random and without replacement from the deck of three cards. The sample space S = {(1, 2), (1, 5), (2, 5)} consists of these three equally likely outcomes. Let X be the total of the two cards drawn. Which of the following is the correct set of probabilities for X?
A) / X / 1 / 2 / 5 B) / X / 3 / 6 / 7
P(X) / 1/3 / 1/3 / 1/3 / P(X) / 1/3 / 1/3 / 1/3
C) / X / 3 / 6 / 7 D) / X / 3 / 6 / 7
P(X) / 3/16 / 6/16 / 7/16 / P(X) / 1/4 / 1/2 / 1/4

A stack of four cards contains two red cards and two black cards. I select two cards, one at a time, and do not replace the first card selected before selecting the second card.

20. / Referring to the information above, consider the events
A = the first card selected is red B = the second card selected is red The events A and B are
A) / independent B) disjoint C) complements D) none of the above
21. / Referring to the information above, consider the events
A = the first card selected is red B = the second card selected is black The events A and B are
A) / independent B) disjoint C) complements D) none of the above
25. / Suppose that A and B are two independent events with P(A) = 0.3 and P(B) = 0.3. P(A È B) is
A) / 0.09 B) 0.51 C) 0.52 D) 0.60
26. / Suppose that A and B are two independent events with P(A) = .2 and P(B) = .4. P(A Ç BC) is
A) / 0.08 B) 0.12 C) 0.52 D) 0.60

An event A will occur with probability 0.5. An event B will occur with probability 0.6. The probability that both A and B will occur is 0.1.

32. / Referring to the information above, the conditional probability of A given B
A) / is 0.3 B) is 0.2 C) is 1/6 D) cannot be determined from the information given
33. / Referring to the information above, we may conclude
A) / that events A and B are independent B) that events A and B are disjoint
C) / that either A or B always occurs D) none of the above
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
39. / In question 38, if a randomly selected person is tested and the result is positive, the probability the individual has the disease is
A) / 0.019 B) 0.020 C) 0.021 D) 0.047

Answer Key

1. / B
2. / A
3. / C
6. / C
7. / C
9. / B
11. / A
12. / C
13. / D
17. / B
19. / B
20. / D
21. / D
25. / B
26. / B
28. / A
29. / C
30. / A
31. / D
32. / C
33. / C
38. / C
39. / D

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