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)100.2200.3300.25400.25

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

x: 10, 20, 30, 40p(x): 0.2, 0.3, 0.25, 0.25
E(X) =
2.Easy
xp(x)0?10.120.330.240.3

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, 0.3, 0.2, 0.3
P(X = 0) =
3.Medium
xp(x)00.3510.320.35μ = 1

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

x: 0, 1, 2p(x): 0.35, 0.3, 0.35
Var(X) =
4.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 =
5.Hard
n = 8, p = 0.5: P(X ≤ 1) = ?k012345678

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

n = 8p = 0.5
P =
6.Hard
xp(x)10.2520.130.340.35μ

X has the distribution shown, and Y = −2X + 5. Find the standard deviation σY of Y.

x: 1, 2, 3, 4p(x): 0.25, 0.1, 0.3, 0.35Y = −2X + 5
σY =

Answer key

  1. 1. E(X) = 25.5
  2. 2. P(X = 0) = 0.1
  3. 3. Var(X) = 0.7
  4. 4. σ = 0.8047
  5. 5. P = 0.03516
  6. 6. σY = 2.356

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