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)100.15200.35300.3400.2

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

x: 10, 20, 30, 40p(x): 0.15, 0.35, 0.3, 0.2
E(X) =
2.Easy
xp(x)00.310.352?

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

x: 0, 1, 2p(x): 0.3, 0.35, ?
P(X = 2) =
3.Medium
xp(x)10.3520.2530.240.2μ = 2.25

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

x: 1, 2, 3, 4p(x): 0.35, 0.25, 0.2, 0.2
σ =
4.Medium
xp(x)10.1520.3530.240.3μ = 2.65

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

x: 1, 2, 3, 4p(x): 0.15, 0.35, 0.2, 0.3
Var(X) =
5.Hard
€p(x)−20.8580.1980.05

A game costs €2 to play. You win €10 with probability 0.1 and €100 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €2€10: p = 0.1€100: p = 0.05
E(G) = €
6.Hard
xp(x)00.110.3520.3530.2μ

X has the distribution shown, and Y = 5X + 20. Find the standard deviation σY of Y.

x: 0, 1, 2, 3p(x): 0.1, 0.35, 0.35, 0.2Y = 5X + 20
σY =

Answer key

  1. 1. E(X) = 25.5
  2. 2. P(X = 2) = 0.35
  3. 3. σ = 1.135
  4. 4. Var(X) = 1.127
  5. 5. E(G) = 4 €
  6. 6. σY = 4.548

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