answer all

Quegion 1 (a) In a certain Pick 4 game. you pay Rst to select a sequence of four digits. such as 2283. If you buy only one ticket and win. your prize is Rs 5000 and your net gain is 4999. We assume that a sequence can be played only once for a draw. (i) Suppose you buy one ticket. Determine the probability of winning. (ii) Construct a table describing the probability distribution and outcomes corresponding to the purchase of one Pick 4 ticket. (iii) It you play this game once every day, determine the mean number of wins in years with exactly 365 days. (iv) It you play this game once every day, determine the probability of winning exactly once in 365 days. (v) Determine the expected value for the purchase of one ticket. (vi) Determine an expression for the probability of winning it you buy 5 tickets every day for 365 days. (vii) Determine an expression for the probability of winning up to 10 times if you buy 5 tickets every day for 365 days. [2+2+2+2+2+2+2 marks] (b) In a survey of a recent IS promotion. ex- students were asked if they owned their own home, rented an apartment / house. or lived with their parents. The table below shows the re - -nses: (i) Determine the probability of selecting one ex-student from this promotion and getting a male who owns his own home. (ii) Determine the probability that one ex-student is selected and that ear-student is a renter given that the exstudent is known to be a male. [2+4 marks]