Independent or mutually exclusive events are important concepts in probability theory. S = spades, H = Hearts, D = Diamonds, C = Clubs. In a standard deck of 52 cards, there exists 4 kings and 4 aces. Suppose you pick three cards without replacement. Let R = red card is drawn, B = blue card is drawn, E = even-numbered card is drawn. Let's say b is how many study both languages: Turning left and turning right are Mutually Exclusive (you can't do both at the same time), Tossing a coin: Heads and Tails are Mutually Exclusive, Cards: Kings and Aces are Mutually Exclusive, Turning left and scratching your head can happen at the same time. E = {HT, HH}. Then \(\text{D} = \{2, 4\}\). P B Difference between mutually exclusive and independent event: At first glance, the definitions of mutually exclusive events and independent events may seem similar to you. Manage Settings The probability of drawing blue is a. Fifty percent of all students in the class have long hair. It consists of four suits. His choices are I = the Interstate and F = Fifth Street. A and B are independent if and only if P (A B) = P (A)P (B) (Answer yes or no.) Check whether \(P(\text{F AND L}) = P(\text{F})P(\text{L})\). Learn more about Stack Overflow the company, and our products. \(\text{A}\) and \(\text{C}\) do not have any numbers in common so \(P(\text{A AND C}) = 0\). That is, event A can occur, or event B can occur, or possibly neither one but they cannot both occur at the same time. This is definitely a case of not Mutually Exclusive (you can study French AND Spanish). Then B = {2, 4, 6}. A and B are mutually exclusive events if they cannot occur at the same time. Remember the equation from earlier: We can extend this to three events as follows: So, P(AnBnC) = P(A)P(B)P(C), as long as the events A, B, and C are all mutually independent, which means: Lets say that you are flipping a fair coin, rolling a fair 6-sided die, and rolling a fair 10-sided die. You have a fair, well-shuffled deck of 52 cards. \(\text{E} =\) even-numbered card is drawn. If the events A and B are not mutually exclusive, the probability of getting A or B that is P (A B) formula is given as follows: Some of the examples of the mutually exclusive events are: Two events are said to be dependent if the occurrence of one event changes the probability of another event.
