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)10.152?30.3540.250.1

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

x: 1, 2, 3, 4, 5p(x): 0.15, ?, 0.35, 0.2, 0.1
P(X = 2) =
2.Easy
sum = 10die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 10?

2 dice= 10
P =
3.Medium
xp(x)100.3200.3300.1400.3μ = 24

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

x: 10, 20, 30, 40p(x): 0.3, 0.3, 0.1, 0.3
σ =
4.Medium
n = 10k = 2N = ?

In how many ways N can a committee of 2 people be chosen from a group of 10? The order does not matter.

n = 10k = 2
N =
5.Hard
n = 7, p = 0.6: P(X ≤ 1) = ?k01234567

7 components are tested, and each one fails with probability 0.6, independently. What is the probability P that at most one fails?

n = 7p = 0.6
P =
6.Hard
xp(x)00.1510.120.2530.3540.15μ

X has the distribution shown, and Y = −2X + 4. Find the standard deviation σY of Y.

x: 0, 1, 2, 3, 4p(x): 0.15, 0.1, 0.25, 0.35, 0.15Y = −2X + 4
σY =

Answer key

  1. 1. P(X = 2) = 0.2
  2. 2. P = 0.08333
  3. 3. σ = 12
  4. 4. N = 45
  5. 5. P = 0.01884
  6. 6. σY = 2.52

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