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
xp(x)00.052?40.3560.3

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

x: 0, 2, 4, 6p(x): 0.05, ?, 0.35, 0.3
P(X = 2) =
2.Easy
red: 8blue: 6green: 2

A bag holds 8 red, 6 blue and 2 green balls. You draw one at random. What is the probability P that it is blue?

8 / 6 / 2
P =
3.Medium
xp(x)10.3520.130.3540.2μ = 2.4

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

x: 1, 2, 3, 4p(x): 0.35, 0.1, 0.35, 0.2
Var(X) =
4.Medium
xp(x)100.1200.2300.35400.35μ = 29.5

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

x: 10, 20, 30, 40p(x): 0.1, 0.2, 0.35, 0.35
σ =
5.Hard
n = 12, p = 0.6: P(X ≤ 1) = ?k0123456789101112

12 components are tested, and each one fails with probability 0.6, independently. What is the probability P that at most one fails?

n = 12p = 0.6
P =
6.Hard
€p(x)−30.68120.3270.02

A game costs €3 to play. You win €15 with probability 0.3 and €30 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €3€15: p = 0.3€30: p = 0.02
E(G) = €

Answer key

  1. 1. P(X = 2) = 0.3
  2. 2. P = 0.375
  3. 3. Var(X) = 1.34
  4. 4. σ = 9.734
  5. 5. P = 0.0003188
  6. 6. E(G) = 2.1 €

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