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: 6blue: 5green: 4

A bag holds 6 red, 5 blue and 4 green balls. You draw one at random. What is the probability P that it is red?

6 / 5 / 4
P =
2.Easy
xp(x)00.2520.240.360.25

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

x: 0, 2, 4, 6p(x): 0.25, 0.2, 0.3, 0.25
E(X) =
3.Medium
xp(x)10.220.2530.340.150.15μ = 2.75

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

x: 1, 2, 3, 4, 5p(x): 0.2, 0.25, 0.3, 0.1, 0.15
Var(X) =
4.Medium
xp(x)00.3510.3520.3μ = 0.95

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

x: 0, 1, 2p(x): 0.35, 0.35, 0.3
σ =
5.Hard
€p(x)−50.7150.25950.05

A game costs €5 to play. You win €20 with probability 0.25 and €100 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €5€20: p = 0.25€100: p = 0.05
E(G) = €
6.Hard
€p(x)−100.8100.15900.05

A game costs €10 to play. You win €20 with probability 0.15 and €100 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €10€20: p = 0.15€100: p = 0.05
E(G) = €

Answer key

  1. 1. P = 0.4
  2. 2. E(X) = 3.1
  3. 3. Var(X) = 1.688
  4. 4. σ = 0.8047
  5. 5. E(G) = 5 €
  6. 6. E(G) = −2 €

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