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)100.35200.2300.1540?

The table gives the probability distribution of X, but one probability is missing. Find P(X = 40).

x: 10, 20, 30, 40p(x): 0.35, 0.2, 0.15, ?
P(X = 40) =
2.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 =
3.Medium
xp(x)00.3510.320.35μ = 1

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

x: 0, 1, 2p(x): 0.35, 0.3, 0.35
σ =
4.Medium
xp(x)00.3510.320.130.1540.1μ = 1.35

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

x: 0, 1, 2, 3, 4p(x): 0.35, 0.3, 0.1, 0.15, 0.1
Var(X) =
5.Hard
xp(x)10.220.0530.3540.0550.35μ

X has the distribution shown, and Y = 2X + 5. Find the standard deviation σY of Y.

x: 1, 2, 3, 4, 5p(x): 0.2, 0.05, 0.35, 0.05, 0.35Y = 2X + 5
σY =
6.Hard
n = 6, p = 0.5: P(X ≤ 1) = ?k0123456

6 components are tested, and each one fails with probability 0.5, independently. What is the probability P that at most one fails?

n = 6p = 0.5
P =

Answer key

  1. 1. P(X = 40) = 0.3
  2. 2. P = 0.1667
  3. 3. σ = 0.8367
  4. 4. Var(X) = 1.827
  5. 5. σY = 2.973
  6. 6. P = 0.1094

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