23+Mutually+inclusive+events

=__Mutually Inclusive Events__ =

//Our topic “Mutually Inclusive Events” has to do, primarily with probability study, and is defined as two events that can occur at the same time, they have common ground (ex: the probability of drawing a playing card that is heart suited or a face, there can be a face card that is heart suited). The goal of out study into this section is to define clearly the difference between mutually inclusive and exclusive events.//

- Any two events in which one cannot happen without the other - In events which aren't mutually exclusive, there is some overlap. - To find the probability of one of the other of two inclusive events, add the probability of the first event to the probability of the second event and subtract the probability of both events happening.

__**General Addition Rule**__
P(A or B) = P(A) + P(B) - P(A and B)

__Examples__
- Since it is possible to get a female puppy that is also brown, these events are inclusive.
 * //1. You choose a puppy at random from a litter of 2 brown males, 1 brown female, 1 black male, and 1 black female.//**
 * //What is the probability of picking a female or a brown puppy?//**

P (female) = 2/5 P(brown) = 3/5 P(female and brown) = 1/5

P(female or brown) = P(female) + P(brown) - P(female and brown) = 2/5 + 3/5 -1/5 = 4/5

//**2. In a classroom, 7 of the 20 girls are seniors, and 4 of the 14 boys are seniors.**// //**What is the probability of randomly selecting a boy or a senior to do their homework?**// - This is mutually inclusive because picking a senior changes the probabilities of picking a boy.

P(A or B) = P(A) + P(B) - P(A and B) =14/34 + 11/34 - 4/34 =21/34 ANSWER

3. You have a 10-sided die, what is the probability that when rolled, an odd number or a prime number shows face up? - this is a mutually inclusive event because there is the possibility of the die showing an odd number that is also a prime number such as 3. P(Odd#)A = 5/10 P(Prime#)B = 4/10 P(A or B) = 3/10 5/10 + 4/10 - 3/10 = 3/5

//**Helpful Links**// [] http://www.lincoln.k12.nv.us/alamo/high/Departments/Math/Module4.htm []