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)100.35200.25300.35400.05

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

x: 10, 20, 30, 40p(x): 0.35, 0.25, 0.35, 0.05
E(X) =
2.Easy
xp(x)1?20.3530.240.2

The table gives the probability distribution of X, but one probability is missing. Find P(X = 1).

x: 1, 2, 3, 4p(x): ?, 0.35, 0.2, 0.2
P(X = 1) =
3.Medium
xp(x)10.320.0530.3540.3μ = 2.65

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

x: 1, 2, 3, 4p(x): 0.3, 0.05, 0.35, 0.3
Var(X) =
4.Medium
P(at least one six) = ??1?2?3?4P(six) = 1/6 on each roll

A fair die is rolled 4 times. What is the probability P of getting at least one six?

n = 4
P =
5.Hard
€p(x)−10.8920.190.01

A game costs €1 to play. You win €3 with probability 0.1 and €10 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €1€3: p = 0.1€10: p = 0.01
E(G) = €
6.Hard
n = 10, p = 0.25: P(X = 4) = ?k012345678910

A test has 10 multiple-choice questions. A student who guesses gets each one right with probability 0.25, independently. What is the probability P of exactly 4 correct answers?

n = 10p = 0.25k = 4
P =

Answer key

  1. 1. E(X) = 21
  2. 2. P(X = 1) = 0.25
  3. 3. Var(X) = 1.428
  4. 4. P = 0.5177
  5. 5. E(G) = −0.6 €
  6. 6. P = 0.146

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