Question 1

If 85% of students wear socks on any given day, and 10 students are chosen at random, what is the probability that all 10 will be wearing socks? Use the binomial probability formula.

Accepted Answer

$$P = (0.85$$)^{10}$$

Question 2

A technician installs motion detectors with an 80% chance of detecting movement. What is the minimum number of sensors needed to have at least a 97% chance that at least one detects movement?

Accepted Answer

$$n = 4$$

Question 3

Tim has an 82% free-throw percentage and shoots 8 balls. What is the expected number of made free throws?

Accepted Answer

$$E = 8 	imes 0.82 = 6.56$$

Question 4

Which is more likely for Tim: making 6 or fewer out of 8 free throws, or making 7 or more out of 8? (Tim's free-throw percentage is 82%)

Accepted Answer

Making 7 or more is more likely

Question 5

Which of the following is NOT a criterion for a binomial experiment?

Accepted Answer

Probability of success changes from trial to trial

Question 6

A person rolls two dice and wins if the sum is 8 or if either die shows a 6. What is the probability of winning on a single roll?

Accepted Answer

$$P = \frac{17}{36}$$

Question 7

A yogurt shipment is accepted if at most 2 out of 16 randomly selected yogurts have open lids. If the probability a lid is on is 95%, what is the probability the shipment is accepted?

Accepted Answer

$$P = \sum_{k=0}^{2} \binom{16}{k} (0.05)^k (0.95$$)^{16-k}$$

Question 8

Sean guesses on a 10-question multiple choice test (4 choices per question). What is the probability he gets at least 6 correct?

Accepted Answer

$$P = \sum_{k=6}^{10} \binom{10}{k} (0.25)^k (0.75$$)^{10-k}$$

Question 9

Dolores chooses 3 pieces of jewelry from a box of 20. How many ways can she select the pieces?

Accepted Answer

$$\binom{20}{3}$$

Question 10

In a class of 30, 3 students are selected to run an errand. How many different combinations are possible?

Accepted Answer

$$\binom{30}{3}$$

Question 11

In a race with 42 runners, 3 prizes are given for 1st, 2nd, and 3rd place. How many different ways can the prizes be awarded?

Accepted Answer

$$P(42,3) = \frac{42!}{(42-3)!}$$

Question 12

Tanya has 8 posters but only room for 5. How many different ways can she arrange 5 posters on the wall?

Accepted Answer

$$P(8,5) = \frac{8!}{(8-5)!}$$

Question 13

A box contains all the letters in 'CAULIFLOWER'. What is the probability of drawing a vowel?

Accepted Answer

$$P = \frac{5}{11}$$

Question 14

From the Venn diagram, what is $$P(S)$$, the probability a randomly chosen person plays Soccer?

Accepted Answer

$$P(S) = \frac{3+2+1+6+5+8}{40} = \frac{25}{40}$$

Question 15

From the Venn diagram, what is $$P(B \cup F)$$, the probability a person plays Baseball or Football?

Accepted Answer

$$P(B \cup F) = \frac{7+3+2+5+1+8}{40} = \frac{26}{40}$$

Question 16

From the Venn diagram, what is $$P(\sim F)$$, the probability a person does NOT play Football?

Accepted Answer

$$P(\sim F) = \frac{7+3+2+6+1}{40} = \frac{19}{40}$$

Question 17

From the Venn diagram, what is $$P(S \cap B)$$, the probability a person plays both Soccer and Baseball?

Accepted Answer

$$P(S \cap B) = \frac{3+2+1}{40} = \frac{6}{40}$$

Question 18

From the Venn diagram, what is $$P(B|F)$$, the probability a person plays Baseball given they play Football?

Accepted Answer

$$P(B|F) = \frac{2+5+1}{5+2+1+8} = \frac{8}{16} = 0.5$$

Precalculus Probability and Counting Principles Study Guide

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