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)00.252?40.3560.15

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

x: 0, 2, 4, 6p(x): 0.25, ?, 0.35, 0.15
P(X = 2) =
2.Easy
xp(x)00.220.2540.256?

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, 0.25, 0.25, ?
P(X = 6) =
3.Medium
xp(x)00.310.3520.2530.1μ = 1.15

For the distribution shown, find the standard deviation σ of X.

x: 0, 1, 2, 3p(x): 0.3, 0.35, 0.25, 0.1
σ =
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
n = 8, p = 0.1: P(X ≤ 1) = ?k012345678

8 components are tested, and each one fails with probability 0.1, independently. What is the probability P that at most one fails?

n = 8p = 0.1
P =
6.Hard
xp(x)100.35200.2300.3400.15μ

X has the distribution shown, and Y = −2X + 1. Find the standard deviation σY of Y.

x: 10, 20, 30, 40p(x): 0.35, 0.2, 0.3, 0.15Y = −2X + 1
σY =

Answer key

  1. 1. P(X = 2) = 0.25
  2. 2. P(X = 6) = 0.3
  3. 3. σ = 0.9631
  4. 4. P = 0.5981
  5. 5. P = 0.8131
  6. 6. σY = 21.79

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