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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Name: ____________________   Date: ____________

1.Easy
sum ≥ 6die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 6?

2 dice≥ 6
P =
2.Easy
xp(x)1?20.330.2540.1

The table gives the probability distribution of X, but one probability is missing. Find P(X = 1).

x: 1, 2, 3, 4p(x): ?, 0.3, 0.25, 0.1
P(X = 1) =
3.Medium
xp(x)100.15200.3300.25400.3μ = 27

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

x: 10, 20, 30, 40p(x): 0.15, 0.3, 0.25, 0.3
σ =
4.Medium
xp(x)00.3520.0540.3560.25μ = 3

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

x: 0, 2, 4, 6p(x): 0.35, 0.05, 0.35, 0.25
Var(X) =
5.Hard
n = 5, p = 0.7: P(X ≤ 1) = ?k012345

5 components are tested, and each one fails with probability 0.7, independently. What is the probability P that at most one fails?

n = 5p = 0.7
P =
6.Hard
€p(x)−10.710.25190.05

A game costs €1 to play. You win €2 with probability 0.25 and €20 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €1€2: p = 0.25€20: p = 0.05
E(G) = €

Answer key

  1. 1. P = 0.7222
  2. 2. P(X = 1) = 0.35
  3. 3. σ = 10.54
  4. 4. Var(X) = 5.8
  5. 5. P = 0.03078
  6. 6. E(G) = 0.5 €

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