question attached

1. (8 points) What is the minimum number of times that Christos should play poker in order to be at least 95% certain that he will be dealt a hand consisting of four-ofakind 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 dene a random variable, X , to denote the deal the number of the rst fourofakind that Christos 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-akind 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 Christos will be dealt a hand consisting of four-of-akind 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. C9 If you do not use R then it might be helpful to recall the identity 2 at = (1 a)_1 for i=0 |a|