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)00.1510.320.3530.2

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

x: 0, 1, 2, 3p(x): 0.15, 0.3, 0.35, 0.2
E(X) =
2.Easy
xp(x)100.3200.05300.3540?

The table gives the probability distribution of X, but one probability is missing. Find P(X = 40).

x: 10, 20, 30, 40p(x): 0.3, 0.05, 0.35, ?
P(X = 40) =
3.Medium
xp(x)10.320.130.240.350.1μ = 2.8

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

x: 1, 2, 3, 4, 5p(x): 0.3, 0.1, 0.2, 0.3, 0.1
Var(X) =
4.Medium
P(at least one six) = ??1?2?3P(six) = 1/6 on each roll

A fair die is rolled 3 times. What is the probability P of getting at least one six?

n = 3
P =
5.Hard
n = 5, p = 0.7: P(X ≤ 1) = ?k012345

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

n = 5p = 0.7
P =
6.Hard
n = 10, p = 0.25: P(X = 4) = ?k012345678910

A test has 10 multiple-choice questions. A student who guesses gets each one right with probability 0.25, independently. What is the probability P of exactly 4 correct answers?

n = 10p = 0.25k = 4
P =

Answer key

  1. 1. E(X) = 1.6
  2. 2. P(X = 40) = 0.3
  3. 3. Var(X) = 1.96
  4. 4. P = 0.4213
  5. 5. P = 0.03078
  6. 6. P = 0.146

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