Mutually Exclusive & Independence PSME 95 – Final Project

Agenda Jennifer Topic Reasons Michaela Mutually Exclusive E.G Aaron Independence E. G + Q

Reasons Mutually exclusive Independence ??

Mutually Exclusive Events Mutually exclusive events cannot logically happen at the same time. They have no outcomes in common. In Statistics it means that the probability of event A and event B is zero. P (A and B) = 0 Example 1: We flip a fair coin. We can either get a head (event A) or a tail (event B). There are two outcomes – head and tail. We logically cannot have a head and a tail at the same time. OR B A Probability of getting a head and a tail at the same time is zero. P (head and tail) = 0 …………..P (A and B) = 0 Events A and B are mutually exclusive. Probability of getting a head is one out of two. P (A) = ½ Probability of getting a tail is one out of two. P(B) = ½

Example 2: Flip 2 fair coins. Event A – getting 2 heads Event B – getting at least 1 head Are events A and B mutually exclusive? Tip: Let your tutee to flip a coin. Solution: List all possible outcomes = {HH, HT, TH, TT} Event A = {HH}, Event B = {HT, TH, HH} Event A and B have 1 outcome in common. P (A and B) ≠ 0 Events A and B are not mutually exclusive. Mutually Exclusive Events HH HT TH Event BEvent A

Independence Independence: Literally, when two events are said to be independent of each other, the occurrence of either one will not affect the probability of another to occur. Vice versa, when the occurrence of either one affects the probability of another to occur, then they are dependent. we have the following formula: and P(A)*P(B)=P(AandB) We are independent, so I won’t affect your existence. Thank you so much!

Question! A fair coin is tossed twice. A head facing up is resulted from the first toss. What is the probability that a head is also facing up in the second toss? 1 st trial: 2 nd trial: ? Lager probability ???

Answer: 0.5!! No matter how many heads you have got from the previous tosses, it still cannot affect the probability of another new trial, in other words, they are independent. A fair coin is tossed twice. A head facing up is resulted from the first toss. What is the probability that a head is also facing up in the second toss? Question!

Mutually Exclusive? Independence? Are they the same thing? Or one implies another? Many students fall into the fraud that mutually exclusive implies that the two events are also independent. However, it is not!! Think about the concept and you will find that when two events are mutually exclusive, the two events should only be dependent of each other. In mathematical interpretation: Given mutually exclusive, then P (A and B) = 0 In the case of independent P(A) * P(B) = P(A and B) thus unless P(A), P(B) are 0, it is impossible for them to be independent. The reasoning is: When two events are mutually exclusive, one’s occurrence eliminate the probability of another to occur, in other words, the occurrence of one has already affected the probability of another to occur. Hence, the two events cannot be independent.

Conclusion Mutually ExclusiveIndependence AB / A B /