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)100.3200.2530?400.35

The table gives the probability distribution of X, but one probability is missing. Find P(X = 30).

x: 10, 20, 30, 40p(x): 0.3, 0.25, ?, 0.35
P(X = 30) =
2.Easy
xp(x)10.3520.0530.0540.250.35

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

x: 1, 2, 3, 4, 5p(x): 0.35, 0.05, 0.05, 0.2, 0.35
E(X) =
3.Medium
xp(x)00.2520.2540.3560.15μ = 2.8

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

x: 0, 2, 4, 6p(x): 0.25, 0.25, 0.35, 0.15
σ =
4.Medium
red: 8blue: 7

A bag holds 8 red and 7 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

8 / 7
P =
5.Hard
xp(x)10.320.230.340.2μ

X has the distribution shown, and Y = 3X − 3. Find the standard deviation σY of Y.

x: 1, 2, 3, 4p(x): 0.3, 0.2, 0.3, 0.2Y = 3X − 3
σY =
6.Hard
€p(x)−50.6950.32450.01

A game costs €5 to play. You win €10 with probability 0.3 and €250 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €5€10: p = 0.3€250: p = 0.01
E(G) = €

Answer key

  1. 1. P(X = 30) = 0.1
  2. 2. E(X) = 3.15
  3. 3. σ = 2.04
  4. 4. P = 0.2667
  5. 5. σY = 3.341
  6. 6. E(G) = 0.5 €

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