Question

1) In a new lottery game called "Minibucks", you select four numbers between 1 and 29. If you match all four numbers with the four numbers chosen by the lottery that day, you win the jackpot. (It doesn't matter whether the order that the lottery selected the numbers matches the order that you selected the numbers). What is the minimum number of different Minibucks tickets you would need to buy for one drawing in order to be 100% certain to win the jackpot for that drawing?

2)In a new lottery game called "Minibucks version 2", you select four numbers between 1 and 11. If you match exactly three of your numbers with the four numbers chosen by the lottery that day, you win $5. What is the probability that you win this prize? Write your answer as a decimal accurate to four decimal places.

3)A drawer contains 14 white socks and 7 black socks. Two different socks are selected from the drawer at random. What is the probability that both of the selected socks are white? Write your answer as a decimal accurate to three decimal places.

Answer 1

1)  minimum number of different Minibucks tickets you would need to buy for one drawing in order to be 100% certain to win the jackpot for that drawing = 29C4 = 23751

2)

P(winning) = 4C3*7C1/11C4 = 0.0848

3) P(both are white) = 14C2 / 21C2 = 0.433