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)10.120.0530.3540.1550.35

A random variable X has the probability distribution shown. Find its expected value E(X).

x: 1, 2, 3, 4, 5p(x): 0.1, 0.05, 0.35, 0.15, 0.35
E(X) =
2.Easy
red: 7blue: 7green: 5

A bag holds 7 red, 7 blue and 5 green balls. You draw one at random. What is the probability P that it is not red?

7 / 7 / 5
P =
3.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 =
4.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 =
5.Hard
xp(x)00.210.220.1530.140.35μ

X has the distribution shown, and Y = 2X − 3. Find the standard deviation σY of Y.

x: 0, 1, 2, 3, 4p(x): 0.2, 0.2, 0.15, 0.1, 0.35Y = 2X − 3
σY =
6.Hard
n = 6, p = 0.3: P(X ≤ 1) = ?k0123456

6 components are tested, and each one fails with probability 0.3, independently. What is the probability P that at most one fails?

n = 6p = 0.3
P =

Answer key

  1. 1. E(X) = 3.6
  2. 2. P = 0.6316
  3. 3. P = 0.7209
  4. 4. P = 0.7674
  5. 5. σY = 3.137
  6. 6. P = 0.4202

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