Independent and Mutually Exclusive Events Quiz

PDF page 197: Two events A and B are independent events if the knowledge that one occurred does not affect the chance the other occurs. For example, the outcomes of two roles of a fair die are independent events. The outcome of the first roll does not change the probability for the outcome of the second roll. To show two events are independent, you must show only one of the above conditions. If two events are not independent, then we say that they are dependent events. Sampling may be done with replacement or without replacement.

PDF page 197: Two events A and B are independent events if the knowledge that one occurred does not affect the chance the other occurs. For example, the outcomes of two roles of a fair die are independent events. The outcome of the first roll does not change the probability for the outcome of the second roll. To show two events are independent, you must show only one of the above conditions. If two events are not independent, then we say that they are dependent events. Sampling may be done with replacement or without replacement.

PDF page 197: of being chosen more than once. When sampling is done with replacement, then events are considered to be independent, meaning the result of the first pick will not change the probabilities for the second pick. A bag contains four blue and three white marbles. James draws one marble from the bag at random, records the color, and 4 replaces the marble. The probability of drawing blue is . When James draws a marble from the bag a second time, the 7 4 probability of drawing blue is still . James replaced the marble after the first draw, so there are still four blue and three 7 white marbles.

PDF page 200: A and B are mutually exclusive events if they cannot occur at the same time. This means that A and B do not share any outcomes and P(A AND B) = 0.

PDF page 200: A and B are mutually exclusive events if they cannot occur at the same time. This means that A and B do not share any outcomes and P(A AND B) = 0.

PDF page 200: and is not equal to zero. Therefore, A and B are not mutually exclusive. 10 A and C do not have any numbers in common so P(A AND C) = 0. Therefore, A and C are mutually exclusive. If it is not known whether A and B are mutually exclusive, assume they are not until you can show otherwise. The following examples illustrate these definitions and terms.

PDF page 200: and is not equal to zero. Therefore, A and B are not mutually exclusive. 10 A and C do not have any numbers in common so P(A AND C) = 0. Therefore, A and C are mutually exclusive. If it is not known whether A and B are mutually exclusive, assume they are not until you can show otherwise. The following examples illustrate these definitions and terms.

PDF page 200: Flip two fair coins. This is an experiment. The sample space is {HH, HT, TH, TT}, where T = tails and H = heads. The outcomes are HH, HT, TH, and TT. The outcomes HT and TH are different. The HT means that the first coin showed heads and the second coin showed tails. The TH means that the first coin showed tails and the second coin showed heads.

PDF page 196: Independent and mutually exclusive do not mean the same thing.

PDF page 201: D = {2, 4}. P(C AND D) = 0 because you cannot have an odd and even face at the same time. Therefore, C and D are mutually exclusive events.

PDF page 202: Suppose P(A) = 0.4 and P(B) = .2. P(A AND B) = .08. Are events A and B independent? Hint—You must show one of

PDF page 202: • P(A AND B) = P(A)P(B)

PDF page 202: and a science class. Suppose P(G) = .6, P(H) = .5, and P(G AND H) = .3. Are G and H independent?

PDF page 202: P(G)P(H) = (.6)(.5) = .3 = P(G AND H)