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)00.2510.32?30.3540.05

The table gives the probability distribution of X, but one probability is missing. Find P(X = 2).

x: 0, 1, 2, 3, 4p(x): 0.25, 0.3, ?, 0.35, 0.05
P(X = 2) =
2.Easy
xp(x)10?200.35300.05400.3

The table gives the probability distribution of X, but one probability is missing. Find P(X = 10).

x: 10, 20, 30, 40p(x): ?, 0.35, 0.05, 0.3
P(X = 10) =
3.Medium
red: 7blue: 6

A bag holds 7 red and 6 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

7 / 6
P =
4.Medium
xp(x)00.3510.320.35μ = 1

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

x: 0, 1, 2p(x): 0.35, 0.3, 0.35
Var(X) =
5.Hard
€p(x)−10.6520.3190.05

A game costs €1 to play. You win €3 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€3: p = 0.3€20: p = 0.05
E(G) = €
6.Hard
xp(x)00.310.3520.35μ

X has the distribution shown, and Y = 0.5X + 5. Find the standard deviation σY of Y.

x: 0, 1, 2p(x): 0.3, 0.35, 0.35Y = 0.5X + 5
σY =

Answer key

  1. 1. P(X = 2) = 0.05
  2. 2. P(X = 10) = 0.3
  3. 3. P = 0.2692
  4. 4. Var(X) = 0.7
  5. 5. E(G) = 0.9 €
  6. 6. σY = 0.4023

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