Please do not give solution in image formate thanku  suppose a national lotto has the following rules: a player chooses 6 numbers between 1 and 42 and pay $1 to play these 6 numbers once. Every week the organizer extract 6 random numbers without replacement between 1 and 42. To win a prize,the player has to guess three or more of the extracted numbers. (a)what is the pdf of X, the number of winning numbers chosen by the player in one week (b)what is the probability to win (any amount)? (c) what is the probability to win, when the player bets every week for a year (consider 52 weeks in a year)? (d) what is the probability that the player needs exactly one year (i.e. 52 weeks) to win? (e) what is the probability that the playee needs no more than one year to win? (f) what is the probability that the playee needs no more than one year but less than 2 years? (g) what is the number of weeks needed such that the probability to win is at least 0.90?

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