Q: In a group, 40% like basketball and 41.4% of football fans like basketball. Are the events 'Likes to watch football' and 'Likes to watch basketball' independent?

No, because $$P(\text{basketball}) \neq P(\text{basketball} | \text{football})$$

Q: Is having a refrigerator and a TV in a dorm room considered mutually exclusive?

No, because $$P(\text{refrigerator and TV}) \neq 0$$

Question 1

Based on the M&M’s color distribution (10% Brown, 10% Red, 20% Yellow, 20% Blue, 20% Orange, rest Green), what is the probability that if you pick four M&M’s in a row, all are Blue? Express your answer as a decimal rounded to four decimal places.

Accepted Answer

$$0.0016$$

Question 2

A box contains 4 medium, 10 large, and 6 extra-large shirts. If you pull out three shirts one at a time without replacement, what is the probability that none of the shirts are extra-large? (Round to four decimal places.)

Accepted Answer

$$0.3193$$

Question 3

Refer to the political party and death penalty table. What is the probability that a randomly chosen voter favors the death penalty?

Accepted Answer

$$0.62$$

Question 4

Using the same table, what is the probability that a randomly chosen Republican favors the death penalty?

Accepted Answer

$$0.867$$

Question 5

Based on the airline passenger table, is being subjected to an additional search independent of carrying a laptop computer?

Accepted Answer

No, because the probability of being searched given carrying a laptop is not equal to the probability of being searched given not carrying a laptop.

Question 6

A survey finds that 10% of families eat turkey, 21% eat ham, and 4% eat both at holiday meals. What is the probability that a randomly selected family had turkey or ham at their holiday meal?

Accepted Answer

$$0.27$$

Question 7

Are having turkey and having ham at holiday meals disjoint (mutually exclusive) events?

Accepted Answer

No, the probability of having turkey and having ham is not equal to zero.

Question 8

A manufacturing firm orders chips from three companies: 10% from A (4% defective), 20% from B (2% defective), and 70% from C (0.5% defective). What is the probability that a randomly selected chip is defective? (Round to four decimal places.)

Accepted Answer

$$0.0115$$

Question 9

Given that a chip is defective, what is the probability it came from Company B? (Round to four decimal places.)

Accepted Answer

$$0.3478$$

Question 10

A poll of 184 teachers finds 57 elementary, 25 middle, and 32 high school teachers favor a policy. 11 elementary, 22 middle, and 37 high school teachers oppose it. Is support for the policy independent of level?

Accepted Answer

No, because 83.8% of elementary teachers are in favor, compared to 62.0% of all teachers in favor.

Question 11

A Covid test has a 99.7% true positive rate and a 98.5% true negative rate. If 14% of patients actually carry Covid, what is the probability that a patient testing negative is truly free of Covid? (Round to four decimal places.)

Accepted Answer

$$0.9995$$

Question 12

A company finds that 60% of workers are married, 52% are college graduates, and 10.92% are both. What is the probability that a randomly chosen worker is married given they are a college graduate? (Round to two decimal places.)

Accepted Answer

$$0.21$$

Question 13

What is the sample space for tossing three coins one after another?

Accepted Answer

$$\{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$$

Question 14

In a group, 40% like basketball and 41.4% of football fans like basketball. Are the events 'Likes to watch football' and 'Likes to watch basketball' independent?

Accepted Answer

No, because $$P(	ext{basketball}) 
eq P(	ext{basketball} | 	ext{football})$$

Question 15

A check of dorm rooms shows 36% have refrigerators, 59% have TVs, and 22% have both. What is the probability that a room has a refrigerator or a TV?

Accepted Answer

$$0.73$$

Question 16

Is having a refrigerator and a TV in a dorm room considered mutually exclusive?

Accepted Answer

No, because $$P(	ext{refrigerator and TV}) 
eq 0$$

Question 17

A junk box contains 14 old batteries, 5 of which are dead. What is the probability that the first two you choose are both good? (Round to three decimal places.)

Accepted Answer

$$0.396$$

Question 18

From the same battery box, what is the probability that at least one of the first three batteries works? (Round to three decimal places.)

Accepted Answer

$$0.973$$

AP Statistics Quiz Review – Probability, Independence, and Conditional Probability

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