Question

An auction website charges $1 for a bid. The bidding starts at 1¢ and goes up 1¢ at a time. A television that is worth $2000 is won, on average, with a bid of $160. You make one bid at random. Find the expected value of the outcome of the bid. (Write as an exact decimal, with a negative sign, if necessary.)

Answer 1

This is fairly complex, but looks like fun.
So first lets count how many bids are made till the bidding goes up to 160.
That is 100*160=16000
How much will be your random bid. Each bid has equal chance so it is the avarge of all bids. (1cent + 160dollars)/2 = 80dollars (rounded)
What is your chance of winning: 1 bid wins out of 16000 so 1/16000.
When you win your profit is 2000-80dollars=1920
1920/16000= 0.12 dollars
You entering the bidding costs 1 dollar and your average win is 0.12
This the outcome is 0.12-1=-0.88 dollars