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)10.320.230.0540.350.15

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

x: 1, 2, 3, 4, 5p(x): 0.3, 0.2, 0.05, 0.3, 0.15
E(X) =
2.Easy
sum ≥ 9die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 9?

2 dice≥ 9
P =
3.Medium
P(at least one six) = ??1?2?3?4?5?6P(six) = 1/6 on each roll

A fair die is rolled 6 times. What is the probability P of getting at least one six?

n = 6
P =
4.Medium
xp(x)00.3510.3520.3μ = 0.95

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

x: 0, 1, 2p(x): 0.35, 0.35, 0.3
Var(X) =
5.Hard
€p(x)−50.65100.3450.05

A game costs €5 to play. You win €15 with probability 0.3 and €50 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €5€15: p = 0.3€50: p = 0.05
E(G) = €
6.Hard
n = 6, p = 0.25: P(X = 5) = ?k0123456

A test has 6 multiple-choice questions. A student who guesses gets each one right with probability 0.25, independently. What is the probability P of exactly 5 correct answers?

n = 6p = 0.25k = 5
P =

Answer key

  1. 1. E(X) = 2.8
  2. 2. P = 0.2778
  3. 3. P = 0.6651
  4. 4. Var(X) = 0.6475
  5. 5. E(G) = 2 €
  6. 6. P = 0.004395

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