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)00.310.252?30.240.1

The table gives the probability distribution of X, but one probability is missing. Find P(X = 2).

x: 0, 1, 2, 3, 4p(x): 0.3, 0.25, ?, 0.2, 0.1
P(X = 2) =
2.Easy
xp(x)10.1520.23?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): 0.15, 0.2, ?, 0.3
P(X = 3) =
3.Medium
red: 7blue: 4

A bag holds 7 red and 4 blue balls. You draw two balls without putting the first one back. What is the probability P that both are red?

7 / 4
P =
4.Medium
xp(x)00.2520.140.3560.3μ = 3.4

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

x: 0, 2, 4, 6p(x): 0.25, 0.1, 0.35, 0.3
Var(X) =
5.Hard
xp(x)10.320.330.0540.35μ

X has the distribution shown, and Y = 2X − 3. Find the standard deviation σY of Y.

x: 1, 2, 3, 4p(x): 0.3, 0.3, 0.05, 0.35Y = 2X − 3
σY =
6.Hard
n = 6, p = 0.7: P(X = 4) = ?k0123456

A test has 6 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 = 6p = 0.7k = 4
P =

Answer key

  1. 1. P(X = 2) = 0.15
  2. 2. P(X = 3) = 0.35
  3. 3. P = 0.3818
  4. 4. Var(X) = 5.24
  5. 5. σY = 2.488
  6. 6. P = 0.3241

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