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.)

Question

Mathematics

Ronald Pratt

3 May, 23:51

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.)

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Keagan Brady · 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