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)10.320.230.154?50.3

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

x: 1, 2, 3, 4, 5p(x): 0.3, 0.2, 0.15, ?, 0.3
P(X = 4) =
2.Easy
xp(x)00.310.3520.35

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

x: 0, 1, 2p(x): 0.3, 0.35, 0.35
E(X) =
3.Medium
n = 8k = 2N = ?

In how many ways N can a committee of 2 people be chosen from a group of 8? The order does not matter.

n = 8k = 2
N =
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)−30.7590.2270.05

A game costs €3 to play. You win €12 with probability 0.2 and €30 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €3€12: p = 0.2€30: p = 0.05
E(G) = €
6.Hard
xp(x)10.0520.330.140.350.25μ

X has the distribution shown, and Y = 0.5X + 20. Find the standard deviation σY of Y.

x: 1, 2, 3, 4, 5p(x): 0.05, 0.3, 0.1, 0.3, 0.25Y = 0.5X + 20
σY =

Answer key

  1. 1. P(X = 4) = 0.05
  2. 2. E(X) = 1.05
  3. 3. N = 28
  4. 4. σ = 0.8047
  5. 5. E(G) = 0.9 €
  6. 6. σY = 0.6403

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