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)10.2520.1530.34?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): 0.25, 0.15, 0.3, ?, 0.1
P(X = 4) =
2.Easy
xp(x)00.351?20.35

The table gives the probability distribution of X, but one probability is missing. Find P(X = 1).

x: 0, 1, 2p(x): 0.35, ?, 0.35
P(X = 1) =
3.Medium
xp(x)10.3520.1530.1540.150.25μ = 2.75

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

x: 1, 2, 3, 4, 5p(x): 0.35, 0.15, 0.15, 0.1, 0.25
Var(X) =
4.Medium
n = 14k = 3N = ?

In how many ways N can a committee of 3 people be chosen from a group of 14? The order does not matter.

n = 14k = 3
N =
5.Hard
n = 8, p = 0.2: P(X = 4) = ?k012345678

A test has 8 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 = 8p = 0.2k = 4
P =
6.Hard
n = 9, p = 0.25: P(X = 3) = ?k0123456789

A test has 9 multiple-choice questions. A student who guesses gets each one right with probability 0.25, independently. What is the probability P of exactly 3 correct answers?

n = 9p = 0.25k = 3
P =

Answer key

  1. 1. P(X = 4) = 0.2
  2. 2. P(X = 1) = 0.3
  3. 3. Var(X) = 2.588
  4. 4. N = 364
  5. 5. P = 0.04588
  6. 6. P = 0.2336

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