Probability worksheet with answers

Free printable Probability worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
xp(x)00.220.340.156?

The table gives the probability distribution of X, but one probability is missing. Find P(X = 6).

x: 0, 2, 4, 6p(x): 0.2, 0.3, 0.15, ?
P(X = 6) =
2.Easy
red: 6blue: 4green: 2

A bag holds 6 red, 4 blue and 2 green balls. You draw one at random. What is the probability P that it is not red?

6 / 4 / 2
P =
3.Medium
red: 4blue: 9

A bag holds 4 red and 9 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

4 / 9
P =
4.Medium
xp(x)100.1200.3300.25400.35μ = 28.5

For the distribution shown, find the variance Var(X) of X.

x: 10, 20, 30, 40p(x): 0.1, 0.3, 0.25, 0.35
Var(X) =
5.Hard
n = 5, p = 0.25: P(X ≤ 1) = ?k012345

5 components are tested, and each one fails with probability 0.25, independently. What is the probability P that at most one fails?

n = 5p = 0.25
P =
6.Hard
n = 7, p = 0.5: P(X ≤ 1) = ?k01234567

7 components are tested, and each one fails with probability 0.5, independently. What is the probability P that at most one fails?

n = 7p = 0.5
P =

Answer key

  1. 1. P(X = 6) = 0.35
  2. 2. P = 0.5
  3. 3. P = 0.07692
  4. 4. Var(X) = 102.8
  5. 5. P = 0.6328
  6. 6. P = 0.0625

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