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)0?20.140.360.3

The table gives the probability distribution of X, but one probability is missing. Find P(X = 0).

x: 0, 2, 4, 6p(x): ?, 0.1, 0.3, 0.3
P(X = 0) =
2.Easy
xp(x)10.3520.130.2540.3

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

x: 1, 2, 3, 4p(x): 0.35, 0.1, 0.25, 0.3
E(X) =
3.Medium
xp(x)00.320.140.2560.35μ = 3.3

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

x: 0, 2, 4, 6p(x): 0.3, 0.1, 0.25, 0.35
σ =
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
n = 11, p = 0.5: P(X = 3) = ?k01234567891011

A test has 11 multiple-choice questions. A student who guesses gets each one right with probability 0.5, independently. What is the probability P of exactly 3 correct answers?

n = 11p = 0.5k = 3
P =
6.Hard
n = 5, p = 0.1: P(X ≤ 1) = ?k012345

5 components are tested, and each one fails with probability 0.1, independently. What is the probability P that at most one fails?

n = 5p = 0.1
P =

Answer key

  1. 1. P(X = 0) = 0.3
  2. 2. E(X) = 2.5
  3. 3. σ = 2.472
  4. 4. Var(X) = 0.6475
  5. 5. P = 0.08057
  6. 6. P = 0.9185

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