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 recipe calls for 2.5 liters of milk. You only have milliliters available. How many milliliters do you need?

$$2.5 \times 1000 = 2500\ \text{mL}$$

Q: A box has a length of 12 cm, width of 5 cm, and height of 8 cm. What is its volume?

$$V = l \times w \times h = 12 \times 5 \times 8 = 480\ \text{cm}^3$$

Q: A weather report states the temperature is 15°C. What is this temperature in Fahrenheit?

$$F = \frac{9}{5} \times 15 + 32 = 27 + 32 = 59^\circ\text{F}$$

Q: A code consists of 3 letters followed by 2 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)

$$26^3$$ \times $$10^2 = 17$$,576 \times 100 = 1,757,600$$

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

$$P = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}$$

Q: A bag contains 4 green, 3 yellow, and 5 red marbles. What are the odds in favor of drawing a yellow marble?

$$\text{Odds in favor} = 3:9 \text{ (correct calculation: 3 yellow, 9 not yellow)}$$

Q: A student randomly selects a number from 1 to 20. What is the probability that the number is a multiple of 4 or 5?

$$P(4) = 5/20$$, $$P(5) = 4/20$$, $$P(4 \text{ and } 5) = 1/20$$;\ P = \frac{5}{20} + \frac{4}{20} - \frac{1}{20} = \frac{8}{20} = 0.4$

Question 1

A hospital needs to select a team of 4 nurses from a group of 10 for a special project. 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 recipe calls for 2.5 liters of milk. You only have milliliters available. How many milliliters do you need?

Accepted Answer

$$2.5 	imes 1000 = 2500\ 	ext{mL}$$

Question 4

A box has a length of 12 cm, width of 5 cm, and height of 8 cm. What is its volume?

Accepted Answer

$$V = l 	imes w 	imes h = 12 	imes 5 	imes 8 = 480\ 	ext{cm}^3$$

Question 5

A weather report states the temperature is 15°C. What is this temperature in Fahrenheit?

Accepted Answer

$$F = \frac{9}{5} 	imes 15 + 32 = 27 + 32 = 59^\circ	ext{F}$$

Question 6

A code consists of 3 letters followed by 2 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

$$26^3$$ 	imes $$10^2 = 17$$,576 	imes 100 = 1,757,600$$

Question 7

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

Accepted Answer

$$P = \frac{1}{2} 	imes \frac{1}{2} 	imes \frac{1}{2} = \frac{1}{8}$$

Question 8

A bag contains 4 green, 3 yellow, and 5 red marbles. What are the odds in favor of drawing a yellow marble?

Accepted Answer

$$	ext{Odds in favor} = 3:9 	ext{ (correct calculation: 3 yellow, 9 not yellow)}$$

Question 9

A student randomly selects a number from 1 to 20. What is the probability that the number is a multiple of 4 or 5?

Accepted Answer

$$P(4) = 5/20$$, $$P(5) = 4/20$$, $$P(4 	ext{ and } 5) = 1/20$$;\ P = \frac{5}{20} + \frac{4}{20} - \frac{1}{20} = \frac{8}{20} = 0.4$

Question 10

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 11

A triangle has a base of 10 cm and a height of 6 cm. What is its area?

Accepted Answer

$$A = \frac{1}{2} 	imes 10 	imes 6 = 30\ 	ext{cm}^2$$

Question 12

A game offers a 30% chance to win $$50, a 50% chance to win 10$$, and a 20% chance to lose $20. What is the expected value?

Accepted Answer

$$E(x) = 50 	imes 0.3 + 10 	imes 0.5 + (-20) 	imes 0.2 = 15 + 5 - 4 = 16$$

Question 13

A school cafeteria offers 5 types of sandwiches, 3 types of drinks, and 4 types of desserts. How many different meal combinations are possible?

Accepted Answer

$$5 	imes 3 	imes 4 = 60$$

Question 14

A student is arranging 5 books on a shelf. In how many different ways can the books be arranged?

Accepted Answer

$$P(5, 5) = 5! = 120$$

Question 15

A medication is packaged in bottles containing 250 milligrams per tablet. How many grams are in 8 tablets?

Accepted Answer

$$8 	imes 250 = 2000\ 	ext{mg};\ 2000 \div 1000 = 2\ 	ext{g}$$

Question 16

A fair die is rolled twice. What is the probability of rolling a 6 both times?

Accepted Answer

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

Question 17

A classroom has 7 boys and 5 girls. If two students are selected 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 rectangular field is 50 meters long and 20 meters wide. What is its area in square meters?

Accepted Answer

$$A = l 	imes w = 50 	imes 20 = 1000\ 	ext{m}^2$$

Question 19

A student has a 0.7 probability of passing a test. What is the probability that the student does NOT pass?

Accepted Answer

$$P(	ext{not pass}) = 1 - 0.7 = 0.3$$

Measurement, Counting Methods, and Probability — Study Guide for Liberal Arts Math

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