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)0?10.320.35

The table gives the probability distribution of X, but one probability is missing. Find P(X = 0).

x: 0, 1, 2p(x): ?, 0.3, 0.35
P(X = 0) =
2.Easy
xp(x)00.320.240.2560.25

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

x: 0, 2, 4, 6p(x): 0.3, 0.2, 0.25, 0.25
E(X) =
3.Medium
xp(x)00.3510.320.35μ = 1

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

x: 0, 1, 2p(x): 0.35, 0.3, 0.35
σ =
4.Medium
red: 6blue: 9

A bag holds 6 red and 9 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

6 / 9
P =
5.Hard
€p(x)−10.6540.3190.05

A game costs €1 to play. You win €5 with probability 0.3 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€5: p = 0.3€20: p = 0.05
E(G) = €
6.Hard
n = 7, p = 0.25: P(X = 2) = ?k01234567

A test has 7 multiple-choice questions. A student who guesses gets each one right with probability 0.25, independently. What is the probability P of exactly 2 correct answers?

n = 7p = 0.25k = 2
P =

Answer key

  1. 1. P(X = 0) = 0.35
  2. 2. E(X) = 2.9
  3. 3. σ = 0.8367
  4. 4. P = 0.1429
  5. 5. E(G) = 1.5 €
  6. 6. P = 0.3115

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