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)00.1510.22?30.35

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

x: 0, 1, 2, 3p(x): 0.15, 0.2, ?, 0.35
P(X = 2) =
2.Easy
sum ≥ 10die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 10?

2 dice≥ 10
P =
3.Medium
xp(x)10.320.230.340.2μ = 2.4

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

x: 1, 2, 3, 4p(x): 0.3, 0.2, 0.3, 0.2
Var(X) =
4.Medium
xp(x)00.310.3520.35μ = 1.05

For the distribution shown, find the standard deviation σ of X.

x: 0, 1, 2p(x): 0.3, 0.35, 0.35
σ =
5.Hard
n = 9, p = 0.7: P(X = 5) = ?k0123456789

A test has 9 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 = 9p = 0.7k = 5
P =
6.Hard
xp(x)10.320.3530.240.15μ

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

x: 1, 2, 3, 4p(x): 0.3, 0.35, 0.2, 0.15Y = 2X − 3
σY =

Answer key

  1. 1. P(X = 2) = 0.3
  2. 2. P = 0.1667
  3. 3. Var(X) = 1.24
  4. 4. σ = 0.8047
  5. 5. P = 0.1715
  6. 6. σY = 2.059

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