Hello everyone!
This really has me stumped. There's a game which is offered by the Washington State lottery called Zip Bingo which costs $2 for one ticket. On
each ticket the player has one set of 35 bingo numbers which are generated randomly and two standard bingo cards called card 1 and card 2. The payoffs are as follows:
Bingo on card 1 --- win $2
Bingo on card 2 --- win $3
Bingo on cards 1 & 2 --- win $5
4 corners on card 1 --- win $10
4 corners on card 2 --- win $15
X on card 1 --- win $25
X on card 2 --- win $35
4 corners on card 1 plus X on card 2 --- win $45
Z on card 1 --- win $100
Z on card 2 --- win $200
Blackout on card 1 --- win $500
Blackout on card 2 --- win $20000

Now, the question is what is the mathematical expectation of this game?
In order to simplify things my calculations are based on the first five payouts only.
Here's my math which must be wrong:
probability of getting a bingo in 35 numbers: 0.27192783.
probability of getting four corners in 35 numbers: 0.043078695.

(0.27192783)*((1-0.043078695)^2)*$2 = $0.498
(0.27192783)*((1-0.043078695)^2)*$3 = $0.747
(0.043078695)*(1-0.043078695)*$10 = $0.412
(0.043078695)*$15 = $0.646

0.498+0.747+0.412+0.646 = $2.30 but each ticket only costs $2!! :confused:

On
each ticket the player has one set of 35 bingo numbers which are generated randomly and two standard bingo cards called card 1 and card 2.

Before getting into the math, how "randomly" generated are these numbers and cards? That your payoff is higher for card 2 than card 1 makes me think the odds are not the same for each. For your typical scratch and win lottery game they choose the number of prizes at each level in advance and print tickets appropriately.

I'm thinkining it's like the "collect letters under the bottle cap to spell COKE" kind of games. They can limit the number of prizes by limiting the number of "K"'s printed, i.e. not all letters are chosen equally.

What's a "standard bingo card"? A 3x3 square?
What are the highest and lowest numbers in the draw?
Do you have a link to the terms and conditions of the game?

The odds are the same for both card 1 and for card 2. The standard bingo card is a 5X5 square with a free space in the middle. The first column has five random numbers selected from 1 to 15, the second column has five random numbers selected from 16 to 30, etc. etc. The ticket has two bingo cards and 35 randomly selected numbers from 1 to 75. You might be able to find information on the Washington State lottery's website.