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)00.3510.32?

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

x: 0, 1, 2p(x): 0.35, 0.3, ?
P(X = 2) =
2.Easy
sum ≥ 5die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 5?

2 dice≥ 5
P =
3.Medium
red: 6blue: 9

A bag holds 6 red and 9 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

6 / 9
P =
4.Medium
xp(x)10.1520.3530.340.2μ = 2.55

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

x: 1, 2, 3, 4p(x): 0.15, 0.35, 0.3, 0.2
σ =
5.Hard
€p(x)−50.79200.2450.01

A game costs €5 to play. You win €25 with probability 0.2 and €50 with probability 0.01; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €5€25: p = 0.2€50: p = 0.01
E(G) = €
6.Hard
n = 8, p = 0.1: P(X = 3) = ?k012345678

A test has 8 multiple-choice questions. A student who guesses gets each one right with probability 0.1, independently. What is the probability P of exactly 3 correct answers?

n = 8p = 0.1k = 3
P =

Answer key

  1. 1. P(X = 2) = 0.35
  2. 2. P = 0.8333
  3. 3. P = 0.1429
  4. 4. σ = 0.9734
  5. 5. E(G) = 0.5 €
  6. 6. P = 0.03307

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