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)100.2200.25300.35400.2

A random variable X has the probability distribution shown. Find its expected value E(X).

x: 10, 20, 30, 40p(x): 0.2, 0.25, 0.35, 0.2
E(X) =
2.Easy
xp(x)10.220.33?40.0550.25

The table gives the probability distribution of X, but one probability is missing. Find P(X = 3).

x: 1, 2, 3, 4, 5p(x): 0.2, 0.3, ?, 0.05, 0.25
P(X = 3) =
3.Medium
xp(x)00.3510.3520.3μ = 0.95

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

x: 0, 1, 2p(x): 0.35, 0.35, 0.3
Var(X) =
4.Medium
xp(x)10.3520.230.340.15μ = 2.25

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

x: 1, 2, 3, 4p(x): 0.35, 0.2, 0.3, 0.15
σ =
5.Hard
xp(x)10.120.330.240.0550.35μ

X has the distribution shown, and Y = 5X − 3. Find the standard deviation σY of Y.

x: 1, 2, 3, 4, 5p(x): 0.1, 0.3, 0.2, 0.05, 0.35Y = 5X − 3
σY =
6.Hard
xp(x)10.1520.330.0540.350.2μ

X has the distribution shown, and Y = 0.5X + 1. Find the standard deviation σY of Y.

x: 1, 2, 3, 4, 5p(x): 0.15, 0.3, 0.05, 0.3, 0.2Y = 0.5X + 1
σY =

Answer key

  1. 1. E(X) = 25.5
  2. 2. P(X = 3) = 0.2
  3. 3. Var(X) = 0.6475
  4. 4. σ = 1.09
  5. 5. σY = 7.224
  6. 6. σY = 0.7053

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