Probability for AP Statistics (page 3)

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By — McGraw-Hill Professional
Updated on Feb 3, 2011

Probability of A and B or A or B

The Addition Rule: P(A or B) = P(A) + P(B) – P(A and B).

Special case of The Addition Rule: If A and B are mutually exclusive,

P(A and B) = 0, so P(A or B) = P(A) + P(B).

The Multiplication Rule: P(A and B) = P(A) · P(B|A).

Special case of The Multiplication Rule: If A and B are independent,

P(B|A) = P(B), so P(A and B) = P(A) · P(B).

example: If A and B are two mutually exclusive events for which P(A) = 0.3, P(B) = 0.25. Find P(A or B).

solution: P(A or B) = 0.3 + 0.25 = 0.55.

example: A basketball player has a 0.6 probability of making a free throw. What is his probability of making two consecutive free throws if

  1. he gets very nervous after making the first shot and his probability of making the second shot drops to 0.4.
  2. solution: P(making the first shot) = 0.6, P(making the second shot | he made the first) = 0.4. So, P(making both shots) = (0.6)(0.4) = 0.24.

  3. the events "he makes his first shot" and "he makes the succeeding shot" are independent.

solution: Since the events are independent, his probability of making each shot is the same. Thus, P(he makes both shots) = (0.6)(0.6) = 0.36.

Practice problems for these concepts can be found at:

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