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)00.351?20.3

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

x: 0, 1, 2p(x): 0.35, ?, 0.3
P(X = 1) =
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: 7blue: 3

A bag holds 7 red and 3 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

7 / 3
P =
4.Medium
xp(x)00.310.3520.35μ = 1.05

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

x: 0, 1, 2p(x): 0.3, 0.35, 0.35
Var(X) =
5.Hard
€p(x)−50.73200.252450.02

A game costs €5 to play. You win €25 with probability 0.25 and €250 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €5€25: p = 0.25€250: p = 0.02
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 = 1) = 0.35
  2. 2. P = 0.8333
  3. 3. P = 0.4667
  4. 4. Var(X) = 0.6475
  5. 5. E(G) = 6.25 €
  6. 6. P = 0.01758

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