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 ≥ 8die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 8?

2 dice≥ 8
P =
2.Easy
xp(x)00.3510.1520.330.140.1

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

x: 0, 1, 2, 3, 4p(x): 0.35, 0.15, 0.3, 0.1, 0.1
E(X) =
3.Medium
xp(x)00.3510.3520.3μ = 0.95

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

x: 0, 1, 2p(x): 0.35, 0.35, 0.3
σ =
4.Medium
P(at least one six) = ??1?2P(six) = 1/6 on each roll

A fair die is rolled 2 times. What is the probability P of getting at least one six?

n = 2
P =
5.Hard
n = 12, p = 0.25: P(X = 5) = ?k0123456789101112

A test has 12 multiple-choice questions. A student who guesses gets each one right with probability 0.25, independently. What is the probability P of exactly 5 correct answers?

n = 12p = 0.25k = 5
P =
6.Hard
n = 10, p = 0.7: P(X = 5) = ?k012345678910

A test has 10 multiple-choice questions. A student who guesses gets each one right with probability 0.7, independently. What is the probability P of exactly 5 correct answers?

n = 10p = 0.7k = 5
P =

Answer key

  1. 1. P = 0.4167
  2. 2. E(X) = 1.45
  3. 3. σ = 0.8047
  4. 4. P = 0.3056
  5. 5. P = 0.1032
  6. 6. P = 0.1029

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