Probability

(21) A bag contains 5 red balls, 3 green balls, and 2 yellow balls. If you draw one ball at random, what is the probability of getting a red ball or a yellow ball?

• (a) \(\frac{5}{10}\)
• (b) \(\frac{7}{10}\)
• (c) \(\frac{3}{10}\)
• (d) \(\frac{2}{10}\)

Answer

Correct Answer: (b) \(\frac{7}{10}\)
P(\text{red or yellow}) = P(\text{red}) + P(\text{yellow}) = \frac{5}{10} + \frac{2}{10} = \frac{7}{10}.

(22) A box contains 6 white marbles, 4 black marbles, and 2 gray marbles. If you randomly select two marbles without replacement, what is the probability that both marbles are gray?

• (a) \(\frac{2}{12}\)
• (b) \(\frac{1}{6}\)
• (c) \(\frac{1}{66}\)
• (d) \(\frac{1}{11}\)

Answer

Correct Answer: (c) \(\frac{1}{66}\)
P(\text{both gray}) = \frac{\text{Number of gray marbles}}{\text{Total number of marbles}} \times \frac{\text{Number of gray marbles - 1}}{\text{Total number of marbles - 1}} = \frac{2}{12} \times \frac{1}{11} = \frac{1}{66}.

(23) In a deck of 52 cards, what is the probability of drawing a face card (jack, queen, or king) at random?

• (a) \(\frac{1}{4}\)
• (b) \(\frac{1}{13}\)
• (c) \(\frac{3}{13}\)
• (d) \(\frac{1}{3}\)

Answer

Correct Answer: (c) \(\frac{3}{13}\)
P(\text{face card}) = \frac{\text{Number of face cards}}{\text{Total number of cards}} = \frac{12}{52} = \frac{3}{13}.

(24) You roll two six-sided dice. What is the probability that the sum of the numbers rolled is 7?

• (a) \(\frac{1}{36}\)
• (b) \(\frac{1}{6}\)
• (c) \(\frac{1}{12}\)
• (d) \(\frac{5}{36}\)

Answer

Correct Answer: (b) \(\frac{1}{6}\)
P(\text{sum is 7}) = P(\{1, 6\}, \{2, 5\}, \{3, 4\}, \{4, 3\}, \{5, 2\}, \{6, 1\}) = \frac{6}{36} = \frac{1}{6}.

(25) In a bag, there are 8 balls, numbered from 1 to 8. If you draw one ball at random, what is the probability that the number on the ball is a prime number?

• (a) \(\frac{4}{8}\)
• (b) \(\frac{1}{4}\)
• (c) \(\frac{3}{8}\)
• (d) \(\frac{2}{8}\)

Answer

Correct Answer: (a) \(\frac{4}{8}\)
P(\text{prime number}) = \frac{\text{Number of prime-numbered balls}}{\text{Total number of balls}} = \frac{4}{8} = \frac{1}{2}.