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Rules of Probability

Probability of Mutually Exclusive Events​

Example: What is the probability of a dice showing 1 or 3?

P(A) = 1/ 6 and P(3) = 1/6

P(1 or 3) = P(1) + P(3) = 1/6 + 1/6 = 2/6 = 1/3

Probability of Mutually Nonexclusive Events​

Example: An urn contains two red, four green, five blue, and three yellow marbles. If a single random marble is chosen from the box, what is the probability that it is a red or green marble?

P(red or gree) = P(red) + p(green) – P(red)*P(green)

= 2/14 + 4/14 – 2/14*4/14 = 0.14 + 0.28 – 0.04 = 0.38

Probability of Mutually Independent Events​

The probability of two mutually independent events happening at the same time is P(X and Y) = P(X) \* P(Y).

The Probability of the Complement​

The probability of event A is P(A) and the probability of its complement, an event not occurring, is P(Ac) = 1 – P(A).

Conditional Probability​

Example

In a group of 100 electronics shopping customers, 40 bought TV (event A), 30 purchased sound systems (event B), and 20 purchased a TV system and a sound system. If a customer chosen at random bought a TV system, what is the probability they also bought sound system?

  • Step 1: P(A) is given in the question as 40 percent, or 0.4.
  • Step 2: P(B) is given that is 0.3.
  • Step 3: P(A∩B), this is the intersection of A and B, purchasing both A and B is 0.2.
  • Step 4: Now use the formula to calculate the conditional probability.
P(B|A) = P(A∩B) / P(A) = 0.2 / 0.4 = 0.5.

The probability that a customer bought a sound system, given that they purchased a TV system, is 50 percent.

Last updated on by sparsh