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)0?10.3520.3

The table gives the probability distribution of X, but one probability is missing. Find P(X = 0).

x: 0, 1, 2p(x): ?, 0.35, 0.3
P(X = 0) =
2.Easy
xp(x)00.2520.34?60.1

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

x: 0, 2, 4, 6p(x): 0.25, 0.3, ?, 0.1
P(X = 4) =
3.Medium
xp(x)00.310.1520.2530.2540.05μ = 1.6

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

x: 0, 1, 2, 3, 4p(x): 0.3, 0.15, 0.25, 0.25, 0.05
σ =
4.Medium
n = 10k = 2N = ?

In how many ways N can a committee of 2 people be chosen from a group of 10? The order does not matter.

n = 10k = 2
N =
5.Hard
€p(x)−50.75100.22450.05

A game costs €5 to play. You win €15 with probability 0.2 and €250 with probability 0.05; otherwise you win nothing. The stake is not returned. Find the expected net gain E(G) per game.

stake = €5€15: p = 0.2€250: p = 0.05
E(G) = €
6.Hard
n = 8, p = 0.3: P(X = 5) = ?k012345678

A test has 8 multiple-choice questions. A student who guesses gets each one right with probability 0.3, independently. What is the probability P of exactly 5 correct answers?

n = 8p = 0.3k = 5
P =

Answer key

  1. 1. P(X = 0) = 0.35
  2. 2. P(X = 4) = 0.35
  3. 3. σ = 1.281
  4. 4. N = 45
  5. 5. E(G) = 10.5 €
  6. 6. P = 0.04668

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