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)100.2200.35300.35400.1

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

x: 10, 20, 30, 40p(x): 0.2, 0.35, 0.35, 0.1
E(X) =
2.Easy
red: 5blue: 6green: 4

A bag holds 5 red, 6 blue and 4 green balls. You draw one at random. What is the probability P that it is not red?

5 / 6 / 4
P =
3.Medium
xp(x)00.1510.2520.0530.2540.3μ = 2.3

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

x: 0, 1, 2, 3, 4p(x): 0.15, 0.25, 0.05, 0.25, 0.3
Var(X) =
4.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 =
5.Hard
n = 10, p = 0.25: P(X = 1) = ?k012345678910

A test has 10 multiple-choice questions. A student who guesses gets each one right with probability 0.25, independently. What is the probability P of exactly 1 correct answers?

n = 10p = 0.25k = 1
P =
6.Hard
n = 12, p = 0.7: P(X ≤ 1) = ?k0123456789101112

12 components are tested, and each one fails with probability 0.7, independently. What is the probability P that at most one fails?

n = 12p = 0.7
P =

Answer key

  1. 1. E(X) = 23.5
  2. 2. P = 0.6667
  3. 3. Var(X) = 2.21
  4. 4. P = 0.5981
  5. 5. P = 0.1877
  6. 6. P = 1.541 × 10⁻⁵

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