Addition Rules of Probability

Probability is the chance or possibility of the occurrence of an event of a particular experiment. Addition rules are used to find the probability that either or both of two events occurs.

Addition rules of probability:

If A and B are mutually exclusive events, then

P(A or B) = P(A) + P(B) otherwise P(A or B) = P(A) + P(B) – P(A and B)
Addition Rules of Probability – Example Problems

Example 1: The probability that Anita will bye a washing machine is `5/11` and the probability that she will bye a one more washing machine is  `7/11`. If the probability of bye at least one washing machine `9/11` , find the probability that she will bye two washing machine.

Solution:

Here P(A) = `5/11` , P(B) = `7/11`

P(A or B) = `9/11` , (P(A and B) = ?

Use addition rules of probability:

P(A or B)  =  P(A) + P(B)  - P(A and B)                                 [Because A and B are not mutualy exclusive events]

`9/11` = `5/11` + `7/11` - P(A and B)

`9/11` = ` 12/11` - P(A and B)

P(A and B) = `12/11` - `9/11` = `3/11`

P(A and B) =  `3/11`

Example 2: Maggi has 8 ten dollar bills and 7 twenty dollar bills. Two bills are drawn at random. Find the probability that two will be of the same kind of bills.

Solution:

Let S = Sample space

A be the event of drawing 2 ten dollar bills.

B be the event of drawing 2 twenty dollar bills.

(A or B) be the event of drawing 2 ten dollar bills or 2 twenty dollar bills.

n(S) = 15C2 = `(15!)/(2!xx13!)` = `(15xx14)/2` = 105

n(A) = 8C2 = `(8!)/(2!xx6!)` = `(8xx7)/2` = 28

n(B) = 7C2 =` (7!)/(2!xx5!)` = `(7xx6)/2` = 21

P(A) = `(n(A))/(n(S))` =`28/105 ` = `4/15`

P(B) =` (n(B))/(n(S))` = `21/105` = `3/15`

P(A or B) = P(A) + P(B)

= `4/15 ` + `3/15` = `7/15`

P(A or B)  = `7/15`



I am planning to write more post on linear equations in one variable examples and solve linear equations with fractions. Keep checking my blog.


Addition Rules of Probability – Practice Problems

Problem 1: The probability that a Danny will sale a mobile is `9/13` and the probability that he will sale a one more mobile is `2/13` . If the probability of sale at least one mobile is `7/13` , find the probability that he will sale two mobiles.

Problem 2: There are 10 lemons and 10 papays. Two fruits are drawn at random. Find the probability that they will be of the same kind.

Answer: 1) `4/13` 2) `9/19`