Probability

(26) You have a deck of 52 cards. What is the probability of drawing a spade (a card with a spade symbol) at random?

• (a) \(\frac{13}{52}\)
• (b) \(\frac{1}{4}\)
• (c) \(\frac{26}{52}\)
• (d) \(\frac{39}{52}\)

Answer

Correct Answer: (a) \(\frac{13}{52}\)
P(\text{spade}) = \frac{\text{Number of spades}}{\text{Total number of cards}} = \frac{13}{52} = \frac{1}{4}.

(27) A bag contains 4 red balls and 5 yellow balls. If you draw one ball at random, what is the probability of getting a red ball?

• (a) \(\frac{4}{9}\)
• (b) \(\frac{5}{9}\)
• (c) \(\frac{1}{2}\)
• (d) \(\frac{9}{4}\)

Answer

Correct Answer: (a) \(\frac{4}{9}\)
P(\text{red}) = \frac{\text{Number of red balls}}{\text{Total number of balls}} = \frac{4}{9}.

(28) A box contains 2 white marbles, 3 black marbles, and 4 gray marbles. If you randomly select three marbles without replacement, what is the probability that all three marbles are black?

• (a) \(\frac{3}{9}\)
• (b) \(\frac{6}{27}\)
• (c) \(\frac{18}{72}\)
• (d) \(\frac{12}{45}\)

Answer

Correct Answer: (c) \(\frac{18}{72}\)
P(\text{all three black}) = \frac{\text{Number of black marbles}}{\text{Total number of marbles}} \times \frac{\text{Number of black marbles - 1}}{\text{Total number of marbles - 1}} \times \frac{\text{Number of black marbles - 2}}{\text{Total number of marbles - 2}} = \frac{3}{9} \times \frac{2}{8} \times \frac{1}{7} = \frac{18}{72}.

(29) You have a jar with 10 candies: 6 are chocolate, and 4 are caramel. If you take two candies at random without replacement, what is the probability that both candies are chocolate?

• (a) \(\frac{15}{45}\)
• (b) \(\frac{12}{45}\)
• (c) \(\frac{18}{45}\)
• (d) \(\frac{21}{45}\)

Answer

Correct Answer: (a) \(\frac{15}{45}\)
P(\text{both chocolate}) = \frac{\text{Number of chocolate candies}}{\text{Total number of candies}} \times \frac{\text{Number of chocolate candies - 1}}{\text{Total number of candies - 1}} = \frac{6}{10} \times \frac{5}{9} = \frac{15}{45}.

(30) You roll a fair six-sided die. What is the probability of rolling a number less than 3?

• (a) \(\frac{1}{6}\)
• (b) \(\frac{1}{2}\)
• (c) \(\frac{1}{3}\)
• (d) \(\frac{2}{3}\)

Answer

Correct Answer: (c) \(\frac{1}{3}\)
P(\text{number less than 3}) = P(\{1, 2\}) = \frac{2}{6} = \frac{1}{3}.