he following are common misconceptions surrounding probability. Identify the mistake each person is making. (a) Deon was reading a journal article when he looked up and told his friend, "Ha! This guy said domestic violence and being poor are independent, but that's ridiculous! Of course you can be poor and experience domestic violence!" He's mixing up independence and being disjoint. He's mixing up P(A|B) and P(B|A). He's assuming independence for events that are not independent. (b) Sebastian was watching cops when he noticed another criminal getting arrested while wearing a hoodie. "Man! Every criminal wears hoodies! They should just tell the cops to go after people in hoodies, and they'll catch all the criminals!" He's assuming criminal and hoodie aren't independent when they actually are. He's mixing up independence and being disjoint. He's assuming criminal and hoodie are independent when they actually aren't. He's mixing up P(criminal|hoodie) with P(hoodie|criminal). (c) While playing poker, Kayla announced, "The probability of four of a kind in aces is (4/52) to the fourth power, since four cards out of the 52 cards are aces. She's assuming each card is independent, but there are only 52 cards, so they're dependent. She's mixing up independence and being disjoint. She's mixing up P(1st card ace | 2nd card ace) with P(2nd card ace | 1st card ace)

Note : Sebastian finds that is P(hoodie I criminal) is high , that is probability of wearing a hoodie for a criminal is high . But that does not mean P(criminal I hoodie) will also be high , which is the probability that the person is a criminal given that he wears hoodie .

(c) She is assuming each card is independent , but there are 52 cards , so they are dependent .

Note : Probability of one ace is 4/52 . But after first draw number of aces remains 3 and total number of cards remains 51, and after second draw number of aces remains 2 and total number of cards remains 50 and so on

Thus probability of 4 aces is (4/52)*(3/51)*(2/50)*(1/49) = 4c4 /52c4