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 ≥ 5die 1die 2112345672234567833456789445678910556789101166789101112P = ?

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

2 dice≥ 5
P =
2.Easy
sum ≥ 9die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 9?

2 dice≥ 9
P =
3.Medium
n = 12k = 5N = ?

In how many ways N can a committee of 5 people be chosen from a group of 12? The order does not matter.

n = 12k = 5
N =
4.Medium
xp(x)100.2200.35300.25400.2μ = 24.5

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

x: 10, 20, 30, 40p(x): 0.2, 0.35, 0.25, 0.2
σ =
5.Hard
n = 6, p = 0.25: P(X ≤ 1) = ?k0123456

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

n = 6p = 0.25
P =
6.Hard
xp(x)100.35200.25300.3400.1μ

X has the distribution shown, and Y = 5X − 3. Find the standard deviation σY of Y.

x: 10, 20, 30, 40p(x): 0.35, 0.25, 0.3, 0.1Y = 5X − 3
σY =

Answer key

  1. 1. P = 0.8333
  2. 2. P = 0.2778
  3. 3. N = 792
  4. 4. σ = 10.23
  5. 5. P = 0.5339
  6. 6. σY = 50.68

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