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)10.220.253?40.150.3

The table gives the probability distribution of X, but one probability is missing. Find P(X = 3).

x: 1, 2, 3, 4, 5p(x): 0.2, 0.25, ?, 0.1, 0.3
P(X = 3) =
2.Easy
red: 5blue: 4

A bag holds 5 red and 4 blue balls. You draw one at random. What is the probability P that it is blue?

5 / 4
P =
3.Medium
n = 6k = 4N = ?

In how many ways N can a committee of 4 people be chosen from a group of 6? The order does not matter.

n = 6k = 4
N =
4.Medium
xp(x)100.35200.2300.35400.1μ = 22

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

x: 10, 20, 30, 40p(x): 0.35, 0.2, 0.35, 0.1
Var(X) =
5.Hard
€p(x)−10.8420.15490.01

A game costs €1 to play. You win €3 with probability 0.15 and €50 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €1€3: p = 0.15€50: p = 0.01
E(G) = €
6.Hard
n = 5, p = 0.3: P(X ≤ 1) = ?k012345

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

n = 5p = 0.3
P =

Answer key

  1. 1. P(X = 3) = 0.15
  2. 2. P = 0.4444
  3. 3. N = 15
  4. 4. Var(X) = 106
  5. 5. E(G) = −0.05 €
  6. 6. P = 0.5282

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