3.3 The Addition Rule
Use the Addition Rule: You select a card from a standard deck of 52 playing cards. Find the probability that the card is a 4 or an ace.
A card that is a 4 cannot be an ace. So the events are mutually exclusive. P (4 or ace) = P(4) + P(ace) = 4/52 + 4/52 = 8/52 = 2/13 =.154
The probability that event A or event B will occur is P(A or B) - P(A) + P(B) - P(A or B)
False, the probability that A or B will occur is P(A or B) = P(A) + P(B) - P(A and B)
If two events are mutually exclusive, why is P (A and B ) = 0?
Because A and B cannot occur at the same time
Determine if mutually exclusive: Event A: Randomly select a blood donor with type O blood. Event B: Randomly select a female blood donor
Because the donor can be a female with type O blood, the events are not mutually exclusive.
Determine if mutually exclusive: Event A: Randomly select a male student. Event B: Randomly select a nursing major.
Because the student can be a a male nursing major, the events are not mutually exclusive.
Sales Volume | Months 0k-24,999 | 3 25k-49,999 | 5 50k-74,999 | 6 75k -99,999 | 7 100k-124,999 | 9 125k-149,999 | 2 150k-179,999 | 3 175k-199,999 | 1 Using the sales pattern, find the probablity that the sales rep will sell between 75k - 124,999 next month
Define events A and B A = {monthly sales between 75k-99,999} and B = {monthly sales between 100k and 124,999} Events are Mutually Exclusive. P(A or B) = P(A) + P(B) = 7/36 + 9/36 = 16/36 =4/9 =.444 (36 is the total number of months)
Determine if mutually exclusive: Event A: Roll a 3 on a die Event B: Roll a 4 on a die
Event A has one outcome, a 3. Event B also has one outcome, a 4. These outcomes cannot occur at the same time, so the events are mutually exclusive
A venn diagram shows one circle labeled PG movies and another not overlapping circle that says G movies. Are the events mutually exclusive?
The events are mutually exclusive, since there are no movies that are rated G and are rated PG.
The Addition Rule (In words)
In words, to find the probability that one event or the other will occur, add the individual probabilities of each event and subtract the probability that they both occur.
Use the addition rule You roll a die. Find the probability of rolling a number less than 3 or rolling an odd number.
The events are not mutually exclusive because 1 is an outcome of both events. P (less than 3 or odd) = P(less than 3) + P(odd) - P(less than 3 and odd) = 2/6+3/6 - 1/6 =4/6 =2/3 =.667
Venn Diagram of Presidents Who won the State of California and an overlapping circle Presidents Who Won the Election. Are they mutually exclusive?
The events are not mutually exclusive, since there is at least 1 president candidate who won the State of California and lost the election.
The Addition Rule
The probablity that events A or B will occur, P(A or B) is given by: P(A or B) = P (A) + P (B) - P(A and B) If events A and B are mutually exclusive then: P(A or B) = P(A) + P (B)
Determine whether the following events are mutually exclusive. Explain your reasoning. Event A: Randomly select a voter who is a registered Republican. Event B: Randomly select a voter who is a registered member of the Reform Party.
These events are mutually exclusive, since it is not possible for a voter to both be a registered Republican and be a registered member of the Reform Party.
Determine whether the following events are mutually exclusive. Explain your reasoning. Event A: Randomly select a female biology major. Event B: Randomly select a biology major who is 21 years old.
These events are not mutually exclusive, since it is possible to select a female biology major who is 21 years old.
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. If two events are mutually exclusive, they have no outcomes in common.
True
Mutally exclusive
Two events A and B are mutally exclusive when A and B cannot occur at the same time. That is, A and B have no outcomes in common. P ( A and B) = 0
