Q: A circular garden has a radius of 7 meters. What is its area?

$$A = \pi r^2$ = \pi \times 7^2$ = 49\pi \approx 153.94\ \text{m}^2$$

Q: A weather forecast gives a 25% chance of snow. What is the probability it will NOT snow?

$$P(\text{not snow}) = 1 - 0.25 = 0.75$$

Q: A code consists of 2 letters followed by 3 digits. How many unique codes can be created if each letter and digit can be used more than once? (Assume 26 letters and 10 digits.)

$$26^2$$ \times $$10^3 = 676$$ \times 1000 = 676{,}000$$

Q: Convert 2.5 kilograms to grams.

$$2.5 \times 1{,}000 = 2{,}500\ \text{g}$$

Q: A rectangular prism has length 10 cm, width 4 cm, and height 3 cm. What is its volume?

$$V = l \times w \times h = 10 \times 4 \times 3 = 120\ \text{cm}^3$$

Q: A fair coin is flipped three times. What is the probability of getting heads all three times?

$$P(\text{heads three times}) = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}$$

Q: A game offers a 1/4 chance to win $$100, a 1/2 chance to win 20$$, and a 1/4 chance to lose $50. What is the expected value?

$$E(x) = 100 \times \frac{1}{4} + 20 \times \frac{1}{2} + (-50) \times \frac{1}{4} = 25 + 10 - 12.5 = 22.5$$

Q: A triangle has a base of 12 cm and a height of 5 cm. What is its area?

$$A = \frac{1}{2} \times b \times h = \frac{1}{2} \times 12 \times 5 = 30\ \text{cm}^2$$

Question 1

A hospital needs to select a team of 4 nurses from a pool of 10. How many different teams can be formed?

Accepted Answer

$$C(10, 4) = \frac{10!}{4!\,6!} = 210$$

Question 2

A circular garden has a radius of 7 meters. What is its area?

Accepted Answer

$$A = \pi r^2$ = \pi 	imes 7^2$ = 49\pi \approx 153.94\ 	ext{m}^2$$

Question 3

A weather forecast gives a 25% chance of snow. What is the probability it will NOT snow?

Accepted Answer

$$P(	ext{not snow}) = 1 - 0.25 = 0.75$$

Question 4

A code consists of 2 letters followed by 3 digits. How many unique codes can be created if each letter and digit can be used more than once? (Assume 26 letters and 10 digits.)

Accepted Answer

$$26^2$$ 	imes $$10^3 = 676$$ 	imes 1000 = 676{,}000$$

Question 5

Convert 2.5 kilograms to grams.

Accepted Answer

$$2.5 	imes 1{,}000 = 2{,}500\ 	ext{g}$$

Question 6

A rectangular prism has length 10 cm, width 4 cm, and height 3 cm. What is its volume?

Accepted Answer

$$V = l 	imes w 	imes h = 10 	imes 4 	imes 3 = 120\ 	ext{cm}^3$$

Question 7

A fair coin is flipped three times. What is the probability of getting heads all three times?

Accepted Answer

$$P(	ext{heads three times}) = \frac{1}{2} 	imes \frac{1}{2} 	imes \frac{1}{2} = \frac{1}{8}$$

Question 8

A committee of 3 is to be chosen from 8 people. In how many ways can this be done?

Accepted Answer

$$C(8, 3) = \frac{8!}{3!\,5!} = 56$$

Question 9

A game offers a 1/4 chance to win $$100, a 1/2 chance to win 20$$, and a 1/4 chance to lose $50. What is the expected value?

Accepted Answer

$$E(x) = 100 	imes \frac{1}{4} + 20 	imes \frac{1}{2} + (-50) 	imes \frac{1}{4} = 25 + 10 - 12.5 = 22.5$$

Question 10

A triangle has a base of 12 cm and a height of 5 cm. What is its area?

Accepted Answer

$$A = \frac{1}{2} 	imes b 	imes h = \frac{1}{2} 	imes 12 	imes 5 = 30\ 	ext{cm}^2$$

Question 11

Convert 95°F to Celsius.

Accepted Answer

$$C = \frac{5}{9}(95 - 32) = \frac{5}{9} 	imes 63 = 35$$

Question 12

A bag contains 5 green, 3 yellow, and 2 red marbles. What are the odds in favor of drawing a yellow marble?

Accepted Answer

$$	ext{Odds in favor} = \frac{3}{10 - 3} = 3:7$$

Question 13

You roll two fair six-sided dice. What is the probability that both dice show a 3?

Accepted Answer

$$P = \frac{1}{6} 	imes \frac{1}{6} = \frac{1}{36}$$

Question 14

A school awards gold, silver, and bronze medals to 3 out of 12 students. How many possible ways can the medals be awarded?

Accepted Answer

$$P(12, 3) = \frac{12!}{9!} = 12 	imes 11 	imes 10 = 1{,}320$$

Question 15

A student randomly selects a number from 1 to 20. What is the probability the number is a multiple of 4?

Accepted Answer

$$	ext{Multiples of 4: } 4, 8, 12, 16, 20 \Rightarrow 5 	ext{ numbers}$$
$$P = \frac{5}{20} = \frac{1}{4}$$

Question 16

A lottery requires you to pick 6 numbers from 49. How many possible combinations are there?

Accepted Answer

$$C(49, 6) = \frac{49!}{6!\,43!} = 13{,}983{,}816$$

Question 17

A classroom has 7 boys and 5 girls. If two students are chosen at random, what is the probability both are girls?

Accepted Answer

$$P = \frac{5}{12} 	imes \frac{4}{11} = \frac{20}{132} = \frac{5}{33}$$

Question 18

A medicine bottle contains 250 mL. How many liters is this?

Accepted Answer

$$250 \div 1{,}000 = 0.25\ 	ext{L}$$

Question 19

A student is randomly assigned a locker from 1 to 100. What is the probability the locker number is a prime number less than 20?

Accepted Answer

$$	ext{Primes less than 20: } 2, 3, 5, 7, 11, 13, 17, 19 \Rightarrow 8 	ext{ numbers}$$
$$P = \frac{8}{100} = 0.08$$

Measurement and Probability: Study Guide for Liberal Arts Math

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