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)00.0510.0520.33?40.3

The table gives the probability distribution of X, but one probability is missing. Find P(X = 3).

x: 0, 1, 2, 3, 4p(x): 0.05, 0.05, 0.3, ?, 0.3
P(X = 3) =
2.Easy
sum = 5die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 5?

2 dice= 5
P =
3.Medium
n = 6k = 3N = ?

In how many ways N can a committee of 3 people be chosen from a group of 6? The order does not matter.

n = 6k = 3
N =
4.Medium
xp(x)00.3510.320.35μ = 1

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

x: 0, 1, 2p(x): 0.35, 0.3, 0.35
σ =
5.Hard
n = 5, p = 0.6: P(X = 3) = ?k012345

A test has 5 multiple-choice questions. A student who guesses gets each one right with probability 0.6, independently. What is the probability P of exactly 3 correct answers?

n = 5p = 0.6k = 3
P =
6.Hard
n = 11, p = 0.5: P(X = 5) = ?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 5 correct answers?

n = 11p = 0.5k = 5
P =

Answer key

  1. 1. P(X = 3) = 0.3
  2. 2. P = 0.1111
  3. 3. N = 20
  4. 4. σ = 0.8367
  5. 5. P = 0.3456
  6. 6. P = 0.2256

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