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)10.220.130.2540.350.15

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

x: 1, 2, 3, 4, 5p(x): 0.2, 0.1, 0.25, 0.3, 0.15
E(X) =
2.Easy
red: 7blue: 8green: 4

A bag holds 7 red, 8 blue and 4 green balls. You draw one at random. What is the probability P that it is blue?

7 / 8 / 4
P =
3.Medium
xp(x)10.320.2530.0540.250.2μ = 2.75

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

x: 1, 2, 3, 4, 5p(x): 0.3, 0.25, 0.05, 0.2, 0.2
σ =
4.Medium
xp(x)00.3520.240.260.25μ = 2.7

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

x: 0, 2, 4, 6p(x): 0.35, 0.2, 0.2, 0.25
Var(X) =
5.Hard
€p(x)−100.8400.15900.05

A game costs €10 to play. You win €50 with probability 0.15 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 = €10€50: p = 0.15€100: p = 0.05
E(G) = €
6.Hard
n = 6, p = 0.3: P(X ≤ 1) = ?k0123456

6 components are tested, and each one fails with probability 0.3, independently. What is the probability P that at most one fails?

n = 6p = 0.3
P =

Answer key

  1. 1. E(X) = 3.1
  2. 2. P = 0.4211
  3. 3. σ = 1.545
  4. 4. Var(X) = 5.71
  5. 5. E(G) = 2.5 €
  6. 6. P = 0.4202

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