A game card is given to every customer visiting a restaurant. From past data, one can assume that the probability that a game card will reveal a winning prize is 0.2. (a) Matthew will collect twenty game cards before finding out the prize-winning cards. Find the probability that out of the twenty game cards that Matthew will collect, at least 4 are prize-winning cards. You are expected to define the appropriate random variable that you use.

Consider a bag that contains 220 coins of which 6 are rare indian pennies. for the given pair of events a and b, complete parts (a) and (b) below. a: when one of the 220 coins is randomly selected, it is one of the 6 indian pennies. b: when another one of the 220 coins is randomly selected (with replacement), it is also one of the 6 indian pennies. a. determine whether events a and b are independent or dependent. b. find p(a and b), the probability that events a and b both occur.