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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Name: ____________________   Date: ____________

1.Easy
sum = 7die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is exactly 7?

2 dice= 7
P =
2.Easy
sum ≥ 3die 1die 2112345672234567833456789445678910556789101166789101112P = ?

Two fair dice are rolled. What is the probability P that the sum is at least 3?

2 dice≥ 3
P =
3.Medium
xp(x)10.2520.3530.3540.05μ = 2.2

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

x: 1, 2, 3, 4p(x): 0.25, 0.35, 0.35, 0.05
σ =
4.Medium
xp(x)10.0520.3530.340.3μ = 2.85

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

x: 1, 2, 3, 4p(x): 0.05, 0.35, 0.3, 0.3
Var(X) =
5.Hard
n = 12, p = 0.5: P(X = 5) = ?k0123456789101112

A test has 12 multiple-choice questions. A student who guesses gets each one right with probability 0.5, independently. What is the probability P of exactly 5 correct answers?

n = 12p = 0.5k = 5
P =
6.Hard
xp(x)00.2510.0520.1530.340.25μ

X has the distribution shown, and Y = 2X + 1. Find the standard deviation σY of Y.

x: 0, 1, 2, 3, 4p(x): 0.25, 0.05, 0.15, 0.3, 0.25Y = 2X + 1
σY =

Answer key

  1. 1. P = 0.1667
  2. 2. P = 0.9722
  3. 3. σ = 0.8718
  4. 4. Var(X) = 0.8275
  5. 5. P = 0.1934
  6. 6. σY = 3.025

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