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)100.3200.25300.1400.35

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

x: 10, 20, 30, 40p(x): 0.3, 0.25, 0.1, 0.35
E(X) =
2.Easy
xp(x)10.3520.33?40.3

The table gives the probability distribution of X, but one probability is missing. Find P(X = 3).

x: 1, 2, 3, 4p(x): 0.35, 0.3, ?, 0.3
P(X = 3) =
3.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 =
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 = 0.1: P(X = 2) = ?k012345678

A test has 8 multiple-choice questions. A student who guesses gets each one right with probability 0.1, independently. What is the probability P of exactly 2 correct answers?

n = 8p = 0.1k = 2
P =
6.Hard
n = 5, p = 0.2: P(X = 3) = ?k012345

A test has 5 multiple-choice questions. A student who guesses gets each one right with probability 0.2, independently. What is the probability P of exactly 3 correct answers?

n = 5p = 0.2k = 3
P =

Answer key

  1. 1. E(X) = 25
  2. 2. P(X = 3) = 0.05
  3. 3. P = 0.4213
  4. 4. P = 0.5177
  5. 5. P = 0.1488
  6. 6. P = 0.0512

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