Selling lottery ticks, $1 tickets each. Each ticket select 5 numbers from 1- 50,

Question

Selling lottery ticks, $1 tickets each. Each ticket select 5 numbers from 1- 50, with no repetition and a Super number from 1-30,inclusive. The prize chart:

Ticket# 02 05 13 23 24
Super# 09

Match.                       Price($)
5 of 5 + Super.          5 Million
5 of 5.                        150,000
Any 4 of 5 + Super. 15 thousand
Any 4 of 5                 500
Any 3 of 5 + Super.   300
Any 3 of 5.                 9
Any 2 of 5 + Super.     20
Any 1 of 5 + Super.   3
Super.                       1

3) if you buy one ticket, what's the probability you'll win a prize? (nearest in cents)

Explanation / Answer

Probability of not winning= (Super didn't match) and (<=2 match)

Prob of not winning= 29/30 * (45C5 +45C4 *5C1 +45C3 *5C2) /(50C5) = 0.9620468

So the probability of winning is 0.03795324 ~ 3.8%

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