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}.