Answer to Question #328377 in Statistics and Probability for jada

Question

Super 6 is one such game. In the game a player selects 6 numbers from 1 – 28. If you match all 6 numbers, you win the Jackpot. If you match 5 out of the 6 numbers, you win $500. If you match 4 out of the 6 numbers, you win $25. There is a separate chamber where you must select 1 of 15 letters from A – O. If you match the correct letter, you win a free ticket.

 

a) How many possible combinations are there for matching all 6 numbers?

b) What is the probability that if you purchase one ticket that you will win the Jackpot?

 

c) What is the probability that if you purchase the lottery that you will win exactly $500?

d) What is the probability that if you purchase the lottery that you will win exactly $25?

 

Answer 1

$a:\\1 combination\,\,with\,\,all\,\,6 numbers\\b:\\1 combination\,\,out\,\,of\,\,C_{28}^{6},\\P=\frac{1}{C_{28}^{6}}=2.65435\times 10^{-6}\\c:\\C_{6}^{5}=6\,\,variants\,\,of\,\,the\,\,set\,\,of\,\,correct\,\,numbers\\28-6=22\,\,variants\,\,of\,\,an\,\,incorrect\,\,number\\P=\frac{6\cdot 22}{C_{28}^{6}}=0.000350374\\d:\\C_{6}^{4}=15\,\,variants\,\,of\,\,the\,\,set\,\,of\,\,correct\,\,numbers\\C_{22}^{2}=231\,\,variants\,\,of\,\,two\,\,incorrect\,\,numbers\\P=\frac{15\cdot 231}{C_{28}^{6}}=0.00919732$