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)00.3510.3520.3

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

x: 0, 1, 2p(x): 0.35, 0.35, 0.3
E(X) =
2.Easy
xp(x)10.3520.130.14?50.1

The table gives the probability distribution of X, but one probability is missing. Find P(X = 4).

x: 1, 2, 3, 4, 5p(x): 0.35, 0.1, 0.1, ?, 0.1
P(X = 4) =
3.Medium
xp(x)00.310.120.2530.35μ = 1.65

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

x: 0, 1, 2, 3p(x): 0.3, 0.1, 0.25, 0.35
Var(X) =
4.Medium
P(at least one six) = ??1?2?3?4?5?6P(six) = 1/6 on each roll

A fair die is rolled 6 times. What is the probability P of getting at least one six?

n = 6
P =
5.Hard
n = 7, p = 0.7: P(X = 1) = ?k01234567

A test has 7 multiple-choice questions. A student who guesses gets each one right with probability 0.7, independently. What is the probability P of exactly 1 correct answers?

n = 7p = 0.7k = 1
P =
6.Hard
n = 11, p = 0.2: P(X = 4) = ?k01234567891011

A test has 11 multiple-choice questions. A student who guesses gets each one right with probability 0.2, independently. What is the probability P of exactly 4 correct answers?

n = 11p = 0.2k = 4
P =

Answer key

  1. 1. E(X) = 0.95
  2. 2. P(X = 4) = 0.35
  3. 3. Var(X) = 1.528
  4. 4. P = 0.6651
  5. 5. P = 0.003572
  6. 6. P = 0.1107

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