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)10.22?30.2540.35

The table gives the probability distribution of X, but one probability is missing. Find P(X = 2).

x: 1, 2, 3, 4p(x): 0.2, ?, 0.25, 0.35
P(X = 2) =
2.Easy
xp(x)10.120.1530.340.355?

The table gives the probability distribution of X, but one probability is missing. Find P(X = 5).

x: 1, 2, 3, 4, 5p(x): 0.1, 0.15, 0.3, 0.35, ?
P(X = 5) =
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
P(at least one six) = ??1?2?3?4?5P(six) = 1/6 on each roll

A fair die is rolled 5 times. What is the probability P of getting at least one six?

n = 5
P =
5.Hard
xp(x)00.210.3520.0530.140.3μ

X has the distribution shown, and Y = 3X + 1. Find the standard deviation σY of Y.

x: 0, 1, 2, 3, 4p(x): 0.2, 0.35, 0.05, 0.1, 0.3Y = 3X + 1
σY =
6.Hard
n = 5, p = 0.5: P(X ≤ 1) = ?k012345

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

n = 5p = 0.5
P =

Answer key

  1. 1. P(X = 2) = 0.2
  2. 2. P(X = 5) = 0.1
  3. 3. P = 0.07692
  4. 4. P = 0.5981
  5. 5. σY = 4.693
  6. 6. P = 0.1875

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