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)0?20.340.160.3

The table gives the probability distribution of X, but one probability is missing. Find P(X = 0).

x: 0, 2, 4, 6p(x): ?, 0.3, 0.1, 0.3
P(X = 0) =
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
P(at least one six) = ??1?2?3?4?5?6?7?8P(six) = 1/6 on each roll

A fair die is rolled 8 times. What is the probability P of getting at least one six?

n = 8
P =
4.Medium
xp(x)100.05200.3300.35400.3μ = 29

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

x: 10, 20, 30, 40p(x): 0.05, 0.3, 0.35, 0.3
Var(X) =
5.Hard
xp(x)00.310.0520.0530.2540.35μ

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

x: 0, 1, 2, 3, 4p(x): 0.3, 0.05, 0.05, 0.25, 0.35Y = 5X − 3
σY =
6.Hard
xp(x)00.2510.120.3530.140.2μ

X has the distribution shown, and Y = −2X + 10. Find the standard deviation σY of Y.

x: 0, 1, 2, 3, 4p(x): 0.25, 0.1, 0.35, 0.1, 0.2Y = −2X + 10
σY =

Answer key

  1. 1. P(X = 0) = 0.3
  2. 2. P = 0.1667
  3. 3. P = 0.7674
  4. 4. Var(X) = 79
  5. 5. σY = 8.382
  6. 6. σY = 2.821

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