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 ≥ 4die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 4?

2 dice≥ 4
P =
2.Easy
xp(x)10.220.230.14?50.35

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

x: 1, 2, 3, 4, 5p(x): 0.2, 0.2, 0.1, ?, 0.35
P(X = 4) =
3.Medium
red: 3blue: 5

A bag holds 3 red and 5 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

3 / 5
P =
4.Medium
xp(x)100.25200.1300.3400.35μ = 27.5

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

x: 10, 20, 30, 40p(x): 0.25, 0.1, 0.3, 0.35
Var(X) =
5.Hard
n = 12, p = 0.4: P(X ≤ 1) = ?k0123456789101112

12 components are tested, and each one fails with probability 0.4, independently. What is the probability P that at most one fails?

n = 12p = 0.4
P =
6.Hard
xp(x)00.0510.3520.0530.340.25μ

X has the distribution shown, and Y = 2X + 5. Find the standard deviation σY of Y.

x: 0, 1, 2, 3, 4p(x): 0.05, 0.35, 0.05, 0.3, 0.25Y = 2X + 5
σY =

Answer key

  1. 1. P = 0.9167
  2. 2. P(X = 4) = 0.15
  3. 3. P = 0.1071
  4. 4. Var(X) = 138.8
  5. 5. P = 0.01959
  6. 6. σY = 2.629

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