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)10.2520.330.34?50.05

The table gives the probability distribution of X, but one probability is missing. Find P(X = 4).

x: 1, 2, 3, 4, 5p(x): 0.25, 0.3, 0.3, ?, 0.05
P(X = 4) =
2.Easy
xp(x)100.3200.130?400.3

The table gives the probability distribution of X, but one probability is missing. Find P(X = 30).

x: 10, 20, 30, 40p(x): 0.3, 0.1, ?, 0.3
P(X = 30) =
3.Medium
P(at least one six) = ??1?2?3?4?5?6?7P(six) = 1/6 on each roll

A fair die is rolled 7 times. What is the probability P of getting at least one six?

n = 7
P =
4.Medium
xp(x)10.1520.2530.340.3μ = 2.75

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

x: 1, 2, 3, 4p(x): 0.15, 0.25, 0.3, 0.3
σ =
5.Hard
xp(x)00.0520.3540.360.3μ

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

x: 0, 2, 4, 6p(x): 0.05, 0.35, 0.3, 0.3Y = −2X + 1
σY =
6.Hard
n = 7, p = 0.5: P(X = 2) = ?k01234567

A test has 7 multiple-choice questions. A student who guesses gets each one right with probability 0.5, independently. What is the probability P of exactly 2 correct answers?

n = 7p = 0.5k = 2
P =

Answer key

  1. 1. P(X = 4) = 0.1
  2. 2. P(X = 30) = 0.3
  3. 3. P = 0.7209
  4. 4. σ = 1.043
  5. 5. σY = 3.639
  6. 6. P = 0.1641

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