subject: The Addition Rule [print this page] Introduction to the addition Rule Introduction to the addition Rule
Probability is the probably that event will happen how likely the event will happen. The addition rule for probability: a statistical property that states the probability of one and/or two events occurring at the same time is equal to the probability of the first event occurring, plus the probability of the second event occurring, minus the probability that both events occur at the same time.
The Addition Rule:
If events A and B are mutually exclusive or disjoint, then P(A U B) = P(A) + P(B)
Otherwise, P(A U B) = P(A) + P(B) P(A B)
Example Problems Based on the Addition Rule
Pro1: Solve using the addition rule in a box of 100 fruits 34 are apples and 43 are oranges. Find the probability that a fruit picked from this box at random is either an apple or orange.
Note that P(apple) = '34/100' and P(orange) = '43/100'
Thus P(apple or orange) = '34/100' + '43/100= ' '77/100'
This makes sense since 77 of the 100 fruits are apples or oranges.
Pro 2: Solve using the addition rule ,In a group of 100 workers 50 are seniors, 60 are male, and 32 are male seniors. Find the probability that a workers picked from this group at random is either a senior or male.
This makes sense since 78 of the 100 workers are seniors or male.
Pro: Solve using the addition rule ,A man goes to the fruit shop. The probability that he checks out a) buying fruits of fiction is 0.50, b) buying fruits of non-fiction is 0.40, and c) both fiction and non-fiction is 0.30. What is the probability that the man checks out buying of fiction, non-fiction, or both?
Solution: Let A = the event that the man checks out fiction; and let B = the event that the man checks out non-fiction. Then, based on the rule of addition
P(A U B) = P(A) + P(B) - P(A B)
P(A U B) = 0.50 + 0.40 - 0.30 = 1.20
Addition Rule
Sum Rule for Probability
A method for finding the probability that either or both of two events occurs.
Addition Rule:
If events A and B are mutually exclusive (disjoint), then
In a group of 101 students 30 are freshmen and 41 are sophomores. Find the probability that a student picked from this group at random is either a freshman or sophomore.
Note that P(freshman) = 30/101 and P(sophomore) = 41/101. Thus
P(freshman or sophomore) = 30/101 + 41/101 = 71/101
This makes sense since 71 of the 101 students are freshmen or sophomores.
Example 2:
not mutually exclusive
In a group of 101 students 40 are juniors, 50 are female, and 22 are female juniors. Find the probability that a student picked from this group at random is either a junior or female.
Note that P(junior) = 40/101 and P(female) = 50/101, and P(junior and female) = 22/101. Thus
P(junior or female) = 40/101 + 50/101 22/101 = 68/101
This makes sense since 68 of the 101 students are juniors or female.
Not sure why? When we add 40 juniors to 50 females and get a total of 90, we have overcounted. The 22 female juniors were counted twice; 90 minus 22 makes 68 students who are juniors or female.
