Probability

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

• (a) $\frac{1}{6}$
• (b) $\frac{1}{12}$
• (c) $\frac{1}{18}$
• (d) $\frac{1}{36}$

Answer

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

(17) A bag contains 8 red balls and 4 green balls. If you draw two balls without replacement, what is the probability that both balls are red?

• (a) $\frac{28}{66}$
• (b) $\frac{4}{12}$
• (c) $\frac{2}{9}$
• (d) $\frac{8}{12}$

Answer

Correct Answer: (a) $\frac{28}{66}$
$P(\text{first red and second red without replacement}) = \frac{8}{12} \cdot \frac{7}{11} = \frac{28}{66}.$

(18) You have a bag with 10 marbles, 3 of which are blue and 7 are red. If you draw one marble and then another marble without replacement, what is the probability that both marbles are red?

• (a) $\frac{7}{10}$
• (b) $\frac{49}{90}$
• (c) $\frac{21}{30}$
• (d) $\frac{14}{30}$

Answer

Correct Answer: (b) $\frac{49}{90}$
$P(\text{first red and second red without replacement}) = \frac{7}{10} \cdot \frac{6}{9} = \frac{42}{90} = \frac{49}{90}.$

(19) You flip a fair coin four times. What is the probability of getting at least one tail?

• (a) $\frac{15}{16}$
• (b) $\frac{1}{16}$
• (c) $\frac{3}{4}$
• (d) $\frac{7}{8}$

Answer

Correct Answer: (a) $\frac{15}{16}$
$P(\text{at least one tail}) = 1 - P(\text{no tails}) = 1 - \left(\frac{1}{2}\right)^4 = 1 - \frac{1}{16} = \frac{15}{16}.$

(20) A spinner is divided into 8 equal sections, numbered 1 through 8. If the spinner is spun once, what is the probability of landing on an even number?

• (a) $\frac{4}{8}$
• (b) $\frac{2}{8}$
• (c) $\frac{3}{8}$
• (d) $\frac{5}{8}$

Answer

Correct Answer: (a) $\frac{4}{8}$
$P(\text{even number}) = \frac{\text{Number of even numbers}}{\text{Total number of sections}} = \frac{4}{8} = \frac{1}{2}.$