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)100.35200.25300.340?

The table gives the probability distribution of X, but one probability is missing. Find P(X = 40).

x: 10, 20, 30, 40p(x): 0.35, 0.25, 0.3, ?
P(X = 40) =
2.Easy
xp(x)10.320.1530.240.2550.1

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

x: 1, 2, 3, 4, 5p(x): 0.3, 0.15, 0.2, 0.25, 0.1
E(X) =
3.Medium
xp(x)00.110.320.230.340.1μ = 2

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

x: 0, 1, 2, 3, 4p(x): 0.1, 0.3, 0.2, 0.3, 0.1
Var(X) =
4.Medium
xp(x)10.220.130.140.350.3μ = 3.4

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

x: 1, 2, 3, 4, 5p(x): 0.2, 0.1, 0.1, 0.3, 0.3
σ =
5.Hard
xp(x)00.2510.320.230.1540.1μ

X has the distribution shown, and Y = 10X + 4. Find the standard deviation σY of Y.

x: 0, 1, 2, 3, 4p(x): 0.25, 0.3, 0.2, 0.15, 0.1Y = 10X + 4
σY =
6.Hard
€p(x)−100.69300.3900.01

A game costs €10 to play. You win €40 with probability 0.3 and €100 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €10€40: p = 0.3€100: p = 0.01
E(G) = €

Answer key

  1. 1. P(X = 40) = 0.1
  2. 2. E(X) = 2.7
  3. 3. Var(X) = 1.4
  4. 4. σ = 1.497
  5. 5. σY = 12.84
  6. 6. E(G) = 3 €

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