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)0?10.320.35

The table gives the probability distribution of X, but one probability is missing. Find P(X = 0).

x: 0, 1, 2p(x): ?, 0.3, 0.35
P(X = 0) =
2.Easy
red: 6blue: 6

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

6 / 6
P =
3.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 =
4.Medium
xp(x)00.2510.0520.2530.3540.1μ = 2

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

x: 0, 1, 2, 3, 4p(x): 0.25, 0.05, 0.25, 0.35, 0.1
Var(X) =
5.Hard
€p(x)−10.8440.15190.01

A game costs €1 to play. You win €5 with probability 0.15 and €20 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €1€5: p = 0.15€20: p = 0.01
E(G) = €
6.Hard
n = 9, p = 0.5: P(X = 1) = ?k0123456789

A test has 9 multiple-choice questions. A student who guesses gets each one right with probability 0.5, independently. What is the probability P of exactly 1 correct answers?

n = 9p = 0.5k = 1
P =

Answer key

  1. 1. P(X = 0) = 0.35
  2. 2. P = 0.5
  3. 3. σ = 0.8047
  4. 4. Var(X) = 1.8
  5. 5. E(G) = −0.05 €
  6. 6. P = 0.01758

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