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
red: 5blue: 4green: 5

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

5 / 4 / 5
P =
2.Easy
xp(x)00.3520.254?60.1

The table gives the probability distribution of X, but one probability is missing. Find P(X = 4).

x: 0, 2, 4, 6p(x): 0.35, 0.25, ?, 0.1
P(X = 4) =
3.Medium
xp(x)100.3200.35300.1400.25μ = 23

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

x: 10, 20, 30, 40p(x): 0.3, 0.35, 0.1, 0.25
Var(X) =
4.Medium
n = 14k = 3N = ?

In how many ways N can a committee of 3 people be chosen from a group of 14? The order does not matter.

n = 14k = 3
N =
5.Hard
€p(x)−100.74400.254900.01

A game costs €10 to play. You win €50 with probability 0.25 and €500 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €10€50: p = 0.25€500: p = 0.01
E(G) = €
6.Hard
n = 9, p = 0.6: P(X ≤ 1) = ?k0123456789

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

n = 9p = 0.6
P =

Answer key

  1. 1. P = 0.2857
  2. 2. P(X = 4) = 0.3
  3. 3. Var(X) = 131
  4. 4. N = 364
  5. 5. E(G) = 7.5 €
  6. 6. P = 0.003801

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