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)10.252?30.3540.35

The table gives the probability distribution of X, but one probability is missing. Find P(X = 2).

x: 1, 2, 3, 4p(x): 0.25, ?, 0.35, 0.35
P(X = 2) =
2.Easy
xp(x)00.3510.320.0530.0540.25

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

x: 0, 1, 2, 3, 4p(x): 0.35, 0.3, 0.05, 0.05, 0.25
E(X) =
3.Medium
xp(x)00.2520.3540.360.1μ = 2.5

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

x: 0, 2, 4, 6p(x): 0.25, 0.35, 0.3, 0.1
Var(X) =
4.Medium
xp(x)00.2510.3520.0530.35μ = 1.5

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

x: 0, 1, 2, 3p(x): 0.25, 0.35, 0.05, 0.35
σ =
5.Hard
n = 11, p = 0.3: P(X = 1) = ?k01234567891011

A test has 11 multiple-choice questions. A student who guesses gets each one right with probability 0.3, independently. What is the probability P of exactly 1 correct answers?

n = 11p = 0.3k = 1
P =
6.Hard
n = 11, p = 0.1: P(X = 5) = ?k01234567891011

A test has 11 multiple-choice questions. A student who guesses gets each one right with probability 0.1, independently. What is the probability P of exactly 5 correct answers?

n = 11p = 0.1k = 5
P =

Answer key

  1. 1. P(X = 2) = 0.05
  2. 2. E(X) = 1.55
  3. 3. Var(X) = 3.55
  4. 4. σ = 1.204
  5. 5. P = 0.09322
  6. 6. P = 0.002455

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