Probability

(6) If three dice are rolled at the same time, what is the probability that all three will land on a different number?

• (a) $\frac{1}{6}$
• (b) $\frac{5}{9}$
• (c) $\frac{1}{3}$
• (d) $\frac{1}{18}$

Answer

Correct Answer: (b) $\frac{5}{9}$
$P(\text{all different}) = \frac{6}{6} \times \frac{5}{6} \times \frac{4}{6} = \frac{5}{9}.$

(7) What is the probability of getting a sum of 7 when two dice are rolled?

• (a) $\frac{5}{36}$
• (b) $\frac{1}{6}$
• (c) $\frac{1}{12}$
• (d) $\frac{1}{8}$

Answer

Correct Answer: (b) $\frac{1}{6}$
$P(\text{sum of 7}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{6}{36} = \frac{1}{6}.$

(8) An urn contains 10 balls: 4 red and 6 blue. If two balls are drawn one after the other with replacement, what is the probability that both are blue?

• (a) $\frac{1}{4}$
• (b) $\frac{9}{25}$
• (c) $\frac{2}{5}$
• (d) $\frac{3}{5}$

Answer

Correct Answer: (b) $\frac{9}{25}$
$P(\text{both blue}) = P(\text{blue first}) \times P(\text{blue second}) = \frac{6}{10} \times \frac{6}{10} = \frac{9}{25}.$

(9) What is the probability that a leap year selected at random will have 53 Sundays?

• (a) $\frac{2}{7}$
• (b) $\frac{2}{7}$
• (c) $\frac{1}{7}$
• (d) $\frac{3}{7}$

Answer

Correct Answer: (b) $\frac{2}{7}$
$P(\text{53 Sundays}) = \frac{\text{Number of weeks with Sunday as first day}}{\text{Total number of weeks}} = \frac{2}{7}.$

(10) What is the probability of selecting a prime number from the set of numbers from 1 to 20?

• (a) $\frac{1}{4}$
• (b) $\frac{8}{20}$
• (c) $\frac{1}{2}$
• (d) $\frac{3}{10}$

Answer

Correct Answer: (b) $\frac{8}{20}$
$P(\text{prime number}) = \frac{\text{Number of primes from 1 to 20}}{\text{Total numbers from 1 to 20}} = \frac{8}{20} = \frac{2}{5}.$