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)00.310.352?

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

x: 0, 1, 2p(x): 0.3, 0.35, ?
P(X = 2) =
2.Easy
xp(x)00.251?20.2530.140.05

The table gives the probability distribution of X, but one probability is missing. Find P(X = 1).

x: 0, 1, 2, 3, 4p(x): 0.25, ?, 0.25, 0.1, 0.05
P(X = 1) =
3.Medium
n = 8k = 4N = ?

In how many ways N can a committee of 4 people be chosen from a group of 8? The order does not matter.

n = 8k = 4
N =
4.Medium
xp(x)00.310.1520.230.35μ = 1.6

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

x: 0, 1, 2, 3p(x): 0.3, 0.15, 0.2, 0.35
Var(X) =
5.Hard
n = 8, p = 0.7: P(X ≤ 1) = ?k012345678

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

n = 8p = 0.7
P =
6.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 =

Answer key

  1. 1. P(X = 2) = 0.35
  2. 2. P(X = 1) = 0.35
  3. 3. N = 70
  4. 4. Var(X) = 1.54
  5. 5. P = 0.00129
  6. 6. P = 0.09322

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