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)00.210.252?30.0540.3

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

x: 0, 1, 2, 3, 4p(x): 0.2, 0.25, ?, 0.05, 0.3
P(X = 2) =
2.Easy
sum = 7die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 7?

2 dice= 7
P =
3.Medium
xp(x)10.220.2530.340.250.05μ = 2.65

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

x: 1, 2, 3, 4, 5p(x): 0.2, 0.25, 0.3, 0.2, 0.05
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
n = 6, p = 0.7: P(X ≤ 1) = ?k0123456

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

n = 6p = 0.7
P =
6.Hard
xp(x)00.3510.320.35μ

X has the distribution shown, and Y = −2X + 20. Find the standard deviation σY of Y.

x: 0, 1, 2p(x): 0.35, 0.3, 0.35Y = −2X + 20
σY =

Answer key

  1. 1. P(X = 2) = 0.2
  2. 2. P = 0.1667
  3. 3. Var(X) = 1.327
  4. 4. P = 0.7209
  5. 5. P = 0.01094
  6. 6. σY = 1.673

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