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)10.320.330.2540.15

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

x: 1, 2, 3, 4p(x): 0.3, 0.3, 0.25, 0.15
E(X) =
2.Easy
xp(x)00.31?20.35

The table gives the probability distribution of X, but one probability is missing. Find P(X = 1).

x: 0, 1, 2p(x): 0.3, ?, 0.35
P(X = 1) =
3.Medium
xp(x)00.210.1520.2530.1540.25μ = 2.1

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

x: 0, 1, 2, 3, 4p(x): 0.2, 0.15, 0.25, 0.15, 0.25
σ =
4.Medium
xp(x)10.3520.2530.0540.35μ = 2.4

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

x: 1, 2, 3, 4p(x): 0.35, 0.25, 0.05, 0.35
Var(X) =
5.Hard
xp(x)100.15200.35300.3400.2μ

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

x: 10, 20, 30, 40p(x): 0.15, 0.35, 0.3, 0.2Y = 2X − 3
σY =
6.Hard
n = 7, p = 0.6: P(X = 3) = ?k01234567

A test has 7 multiple-choice questions. A student who guesses gets each one right with probability 0.6, independently. What is the probability P of exactly 3 correct answers?

n = 7p = 0.6k = 3
P =

Answer key

  1. 1. E(X) = 2.25
  2. 2. P(X = 1) = 0.35
  3. 3. σ = 1.446
  4. 4. Var(X) = 1.64
  5. 5. σY = 19.47
  6. 6. P = 0.1935

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