Probability as Expectation Math Example 1

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Example 1

easy
A basketball player makes free throws with probability 0.75. In 200 free throws, how many do we expect her to make?

Solution

  1. 1
    Expected count formula: E=n×PE = n \times P
  2. 2
    Substitute: E=200×0.75=150E = 200 \times 0.75 = 150
  3. 3
    Interpretation: on average, she will make 150 of 200 free throws
  4. 4
    Note: this is the long-run average — any single game of 200 shots might yield slightly more or fewer

Answer

Expected makes =200×0.75=150= 200 \times 0.75 = 150 free throws.
Expected count =n×P= n \times P gives the average number of successes in nn trials with probability PP. This is the long-run mean of repeated experiments, not a guaranteed exact count for any single trial.

About Probability as Expectation

Probability can be interpreted as the long-run relative frequency of an event over infinitely many identical trials of a random experiment.

Learn more about Probability as Expectation →

More Probability as Expectation Examples

Example 2 medium

A game has three outcomes: win [formula]0 (prob 0.5), lose $5 (prob 0.3). Calculate the expected val

Example 3 easy

A school expects 15% of students to be absent on any given day. If there are 300 students, how many

Example 4 hard

An insurance company charges [formula]10,000 if the insured event occurs (probability 0.01) and $0 o

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