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
sum ≥ 6die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 6?

2 dice≥ 6
P =
2.Easy
xp(x)10.3520.3530.054?50.15

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

x: 1, 2, 3, 4, 5p(x): 0.35, 0.35, 0.05, ?, 0.15
P(X = 4) =
3.Medium
xp(x)00.3520.340.1560.2μ = 2.4

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

x: 0, 2, 4, 6p(x): 0.35, 0.3, 0.15, 0.2
Var(X) =
4.Medium
P(at least one six) = ??1?2?3?4?5?6?7P(six) = 1/6 on each roll

A fair die is rolled 7 times. What is the probability P of getting at least one six?

n = 7
P =
5.Hard
xp(x)00.310.3520.0530.1540.15μ

X has the distribution shown, and Y = 5X + 1. Find the standard deviation σY of Y.

x: 0, 1, 2, 3, 4p(x): 0.3, 0.35, 0.05, 0.15, 0.15Y = 5X + 1
σY =
6.Hard
n = 11, p = 0.7: P(X ≤ 1) = ?k01234567891011

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

n = 11p = 0.7
P =

Answer key

  1. 1. P = 0.7222
  2. 2. P(X = 4) = 0.1
  3. 3. Var(X) = 5.04
  4. 4. P = 0.7209
  5. 5. σY = 7.159
  6. 6. P = 4.724 × 10⁻⁵

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