Probability Questions

Multiple choice
  1. $\dfrac {15}{26}$
  2. $\dfrac {11}{26}$
  3. $\dfrac {1}{2}$
  4. $\dfrac {17}{26}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A standard deck has 52 cards. There are 26 black cards, 4 kings, and 4 queens. Since the 2 black kings and 2 black queens are already counted in the 26 black cards, we subtract the 26 black cards, the 2 red kings, and the 2 red queens, totaling 30 cards to exclude. This leaves 22 cards, and 22/52 simplifies to 11/26.

Multiple choice
  1. $\displaystyle \frac{14}{15}$
  2. $\displaystyle \frac{11}{15}$
  3. $\displaystyle \frac{7}{15}$
  4. $\displaystyle \frac{4}{15}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total balls = 15. Ways to pick 2 balls = 15C2 = 105. Ways to pick 2 red = 8C2 = 28. Ways to pick 2 black = 7C2 = 21. Total favorable ways = 28 + 21 = 49. Probability = 49/105 = 7/15.

Multiple choice
  1. $\displaystyle \frac{1}{2}$
  2. $\displaystyle \frac{1}{4}$
  3. $\displaystyle \frac{1}{3}$
  4. $\displaystyle \frac{1}{5}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let D be Diana's age and J be Jim's age. 3D = 2J + 17. D + J = (3J) - 13. From the second eq: D = 2J - 13. Substitute into the first: 3(2J - 13) = 2J + 17 => 6J - 39 = 2J + 17 => 4J = 56 => J = 14. Then D = 2(14) - 13 = 15. Ages are 15 and 14.

Multiple choice
  1. $\displaystyle \frac{4}{19}$
  2. $\displaystyle \frac{5}{19}$
  3. $\displaystyle \frac{6}{19}$
  4. $\displaystyle \frac{7}{19}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The numbers divisible by 3 between 1 and 19 are 3, 6, 9, 12, 15, and 18. There are 6 such numbers, so the probability is 6/19.

Multiple choice
  1. $ \displaystyle \frac{5}{12} $
  2. $ \displaystyle \frac{3}{13} $
  3. $ \displaystyle \frac{2}{11} $
  4. $ \displaystyle \frac{6}{13} $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total cards = 52. Red cards = 26. Queens = 4. Red Queens = 2. Cards that are red or a queen = 26 + 4 - 2 = 28. Cards that are neither = 52 - 28 = 24. Probability = 24/52 = 6/13.