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)00.0510.1520.2530.354?

The table gives the probability distribution of X, but one probability is missing. Find P(X = 4).

x: 0, 1, 2, 3, 4p(x): 0.05, 0.15, 0.25, 0.35, ?
P(X = 4) =
2.Easy
xp(x)0?10.120.3530.340.2

The table gives the probability distribution of X, but one probability is missing. Find P(X = 0).

x: 0, 1, 2, 3, 4p(x): ?, 0.1, 0.35, 0.3, 0.2
P(X = 0) =
3.Medium
xp(x)00.3510.3520.3μ = 0.95

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

x: 0, 1, 2p(x): 0.35, 0.35, 0.3
σ =
4.Medium
P(at least one six) = ??1?2?3P(six) = 1/6 on each roll

A fair die is rolled 3 times. What is the probability P of getting at least one six?

n = 3
P =
5.Hard
xp(x)00.310.3520.35μ

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

x: 0, 1, 2p(x): 0.3, 0.35, 0.35Y = −2X + 1
σY =
6.Hard
xp(x)00.3510.320.35μ

X has the distribution shown, and Y = −2X + 10. Find the standard deviation σY of Y.

x: 0, 1, 2p(x): 0.35, 0.3, 0.35Y = −2X + 10
σY =

Answer key

  1. 1. P(X = 4) = 0.2
  2. 2. P(X = 0) = 0.05
  3. 3. σ = 0.8047
  4. 4. P = 0.4213
  5. 5. σY = 1.609
  6. 6. σY = 1.673

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