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
sum = 6die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 6?

2 dice= 6
P =
2.Easy
xp(x)100.3200.2300.2400.3

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

x: 10, 20, 30, 40p(x): 0.3, 0.2, 0.2, 0.3
E(X) =
3.Medium
P(at least one six) = ??1?2?3?4?5P(six) = 1/6 on each roll

A fair die is rolled 5 times. What is the probability P of getting at least one six?

n = 5
P =
4.Medium
xp(x)00.3520.3540.0560.25μ = 2.4

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

x: 0, 2, 4, 6p(x): 0.35, 0.35, 0.05, 0.25
Var(X) =
5.Hard
€p(x)−20.8840.1980.02

A game costs €2 to play. You win €6 with probability 0.1 and €100 with probability 0.02; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €2€6: p = 0.1€100: p = 0.02
E(G) = €
6.Hard
n = 9, p = 0.2: P(X = 3) = ?k0123456789

A test has 9 multiple-choice questions. A student who guesses gets each one right with probability 0.2, independently. What is the probability P of exactly 3 correct answers?

n = 9p = 0.2k = 3
P =

Answer key

  1. 1. P = 0.1389
  2. 2. E(X) = 25
  3. 3. P = 0.5981
  4. 4. Var(X) = 5.44
  5. 5. E(G) = 0.6 €
  6. 6. P = 0.1762

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