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)0?10.3520.3

The table gives the probability distribution of X, but one probability is missing. Find P(X = 0).

x: 0, 1, 2p(x): ?, 0.35, 0.3
P(X = 0) =
2.Easy
xp(x)00.3510.320.35

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

x: 0, 1, 2p(x): 0.35, 0.3, 0.35
E(X) =
3.Medium
xp(x)100.15200.2300.3400.35μ = 28.5

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

x: 10, 20, 30, 40p(x): 0.15, 0.2, 0.3, 0.35
Var(X) =
4.Medium
red: 7blue: 9

A bag holds 7 red and 9 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

7 / 9
P =
5.Hard
n = 12, p = 0.7: P(X = 4) = ?k0123456789101112

A test has 12 multiple-choice questions. A student who guesses gets each one right with probability 0.7, independently. What is the probability P of exactly 4 correct answers?

n = 12p = 0.7k = 4
P =
6.Hard
n = 12, p = 0.7: P(X = 5) = ?k0123456789101112

A test has 12 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 = 12p = 0.7k = 5
P =

Answer key

  1. 1. P(X = 0) = 0.35
  2. 2. E(X) = 1
  3. 3. Var(X) = 112.8
  4. 4. P = 0.175
  5. 5. P = 0.007798
  6. 6. P = 0.02911

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