At the county fair, a clown is sitting at a table with three cards in front of h
ID: 3047454 • Letter: A
Question
At the county fair, a clown is sitting at a table with three cards in front of her. She shows you that the first card is red on both sides, the second is white on both sides, and the third is red on one side and white on the other. She picks up the cards, shuffles, hides them in a hat, and then drawas out a card at random and lays it on the table, in such a manner that both of you can see only one side of the card. She says, "This card is red on the side we see. So it's either the red/red card or the red/white card. I'll be you one dollar that the other side is red." Is this a safe bet for you to take? Hint: It's not 1/2.
Explanation / Answer
P(top side is red) =P(red/red card and top side red+red/white card and top side is red)
=(1/3)*(1)+(1/3)*(1/2) =1/2
therefore probability that you win =P(second side white|top side red)
=P(red/white card and top side is red)/P(top side is red) =(1/3)*(1/2)/(1/2 )=1/3
as probability of your winning is less than 1/2 ; this is not safe bet for you to take.
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