- #1
O Great One
- 98
- 0
Hello everyone,
This really has me stumped! The Washington state lottery has a new game called Zip Bingo. Every ticket costs $2 and consists of 2 regular Bingo cards with 35 call numbers. The prizes are as follows:
Regular bingo on card 1: $2
Regular bingo on card 2: $3
Regular bingo on both card 1 and card 2: $5
Match 4 corners on card 1: $10
Match 4 corners on card 2: $15
Match X pattern on card 1: $25
Match X pattern on card 2: $35
Match 4 corners on card 1 and X pattern on card 2: $45
Match Z pattern on card 1: $100
Match Z pattern on card 2: $200
Blackout on card 1: $500
Blackout on card 2: $20,000
Only one prize per ticket.
I tried to calculate the average return from this game, and in order to simplify things just considered the regular bingo and the four corners. It seems a little bit tricky because the events are not mutually exclusive.
The probability of a bingo with 35 numbers is 0.271983.
The probability of getting all four corners with 35 numbers is 0.043078695.
So:
(0.271983)*((1-0.043078695)^2)*2 = 0.50
(0.271983)*((1-0.043078695)^2)*3 = 0.75
(0.043078695)*(1-0.043078695)*10 = 0.41
(0.043078695)*15 = 0.65
0.50 + 0.75 + 0.41 + 0.65 = $2.31 but each ticket only costs $2!
So, where did I go wrong in my math?
This really has me stumped! The Washington state lottery has a new game called Zip Bingo. Every ticket costs $2 and consists of 2 regular Bingo cards with 35 call numbers. The prizes are as follows:
Regular bingo on card 1: $2
Regular bingo on card 2: $3
Regular bingo on both card 1 and card 2: $5
Match 4 corners on card 1: $10
Match 4 corners on card 2: $15
Match X pattern on card 1: $25
Match X pattern on card 2: $35
Match 4 corners on card 1 and X pattern on card 2: $45
Match Z pattern on card 1: $100
Match Z pattern on card 2: $200
Blackout on card 1: $500
Blackout on card 2: $20,000
Only one prize per ticket.
I tried to calculate the average return from this game, and in order to simplify things just considered the regular bingo and the four corners. It seems a little bit tricky because the events are not mutually exclusive.
The probability of a bingo with 35 numbers is 0.271983.
The probability of getting all four corners with 35 numbers is 0.043078695.
So:
(0.271983)*((1-0.043078695)^2)*2 = 0.50
(0.271983)*((1-0.043078695)^2)*3 = 0.75
(0.043078695)*(1-0.043078695)*10 = 0.41
(0.043078695)*15 = 0.65
0.50 + 0.75 + 0.41 + 0.65 = $2.31 but each ticket only costs $2!
So, where did I go wrong in my math?