Answer Happy

ISE 2024 1. Erhan loves to play Poker. Erhan has realized that he has not been dealt a four-of-a-kind hand in a long time and now he wonders what the minimum number of times that he should play poker in order to be at least 95% certain that he will be dealt a hand consisting of four-of-a-kind and one other card? Hints: • Characteristics of a deck of cards and a poker hand: There are 52 cards in a deck, there are 4 suits of cards in a deck, there are 13 ranks of cards in a deck, there are 5 cards in a hand of cards. • It is probably best to start by computing the probability of a hand consisting of four-of- a-kind and one other card. • Next you should probably define a random variable, X, to denote the deal the number of the first four-of-a-kind that Erhan experiences and then its distribution. Look at the distribution of X to see if it is a familiar distribution. • Now think about the meaning of the statement "at least 95% certain that he will be dealt a hand consisting of four-of-a-kind and one other card?" and write this statement in mathematics. • Now solve for k, the minimum number of hands to be dealt in order to be at least 95% certain that Erhan will be dealt a hand consisting of four-of-a-kind and one other card. • It is o.k. to use R to evaluate your solution; but make sure that you include a "snip- and-paste” copy of your R code and solution. • If you do not use R then it might be helpful to recall the identity į ai = (1 – a)-1 for |al < 1 even when for complicated values of a, for instance a= (1 – p)?). i=0