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 = 3die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 3?

2 dice= 3
P =
2.Easy
xp(x)00.3510.0520.2530.35

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

x: 0, 1, 2, 3p(x): 0.35, 0.05, 0.25, 0.35
E(X) =
3.Medium
xp(x)100.3200.25300.35400.1μ = 22.5

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

x: 10, 20, 30, 40p(x): 0.3, 0.25, 0.35, 0.1
σ =
4.Medium
P(at least one six) = ??1?2?3?4P(six) = 1/6 on each roll

A fair die is rolled 4 times. What is the probability P of getting at least one six?

n = 4
P =
5.Hard
n = 8, p = 0.4: P(X ≤ 1) = ?k012345678

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

n = 8p = 0.4
P =
6.Hard
n = 6, p = 0.4: P(X ≤ 1) = ?k0123456

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

n = 6p = 0.4
P =

Answer key

  1. 1. P = 0.05556
  2. 2. E(X) = 1.6
  3. 3. σ = 9.937
  4. 4. P = 0.5177
  5. 5. P = 0.1064
  6. 6. P = 0.2333

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