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)10.3520.3530.154?

The table gives the probability distribution of X, but one probability is missing. Find P(X = 4).

x: 1, 2, 3, 4p(x): 0.35, 0.35, 0.15, ?
P(X = 4) =
2.Easy
xp(x)10.2520.1530.340.2550.05

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

x: 1, 2, 3, 4, 5p(x): 0.25, 0.15, 0.3, 0.25, 0.05
E(X) =
3.Medium
xp(x)00.2510.220.0530.3540.15μ = 1.95

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

x: 0, 1, 2, 3, 4p(x): 0.25, 0.2, 0.05, 0.35, 0.15
σ =
4.Medium
n = 11k = 4N = ?

In how many ways N can a committee of 4 people be chosen from a group of 11? The order does not matter.

n = 11k = 4
N =
5.Hard
n = 5, p = 0.25: P(X = 4) = ?k012345

A test has 5 multiple-choice questions. A student who guesses gets each one right with probability 0.25, independently. What is the probability P of exactly 4 correct answers?

n = 5p = 0.25k = 4
P =
6.Hard
n = 10, p = 0.25: P(X ≤ 1) = ?k012345678910

10 components are tested, and each one fails with probability 0.25, independently. What is the probability P that at most one fails?

n = 10p = 0.25
P =

Answer key

  1. 1. P(X = 4) = 0.15
  2. 2. E(X) = 2.7
  3. 3. σ = 1.465
  4. 4. N = 330
  5. 5. P = 0.01465
  6. 6. P = 0.244

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