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

Question.
If 1 million tickets are sold, what's the probability:
A. nobody wins 5Mill $
B. exactly 1 person wins 5 mill$
C. ATLEAST 1 person wins 5 mill$

prize, if any, will be determined by Prize $5,000,000 $150,000 Match 5 of 5 + Super 5 of 5 Any 4 of 5 + Super $15,000 Any 4 of 5 Any 3 of 5 + Super $300 $500 $9 Any 3 of 5 Any 2 of 5 + Super $20 Any 1 of 5 + Super $3 Super $1 on the information, an Let the random variable

Explanation / Answer

For winning 5 million, the 5 numbers selected from 50 must be the same as the 5 number drawn and the the super number also must match

The probability of such an event = 1/50C5 x 1/30

= 1.573 x 10-8

If 1 million tickets are sold,

A) P(nobody will 5 million)

= (1 - 1.573x10-8 )^1,000,000

= 0.9844

B) P(exactly 1 person winning 5 million) = 1,000,000 x 1.573x10-8 x (1 - 1.573x10-8 )^999,999

= 0.0155

C) P(at least one person will win) = 1 - P(nobody will win)

= 1 - 0.9844

= 0.0156

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