A gambler has four cards—two diamonds and two clubs. The gambler proposes the following game to you: You will leave the room and the gambler will put the cards face down on a table. When you return to...

A gambler has four cards—two diamonds and two clubs. The gambler proposes the following game to you: You will leave the room and the gambler will put the cards face down on a table. When you return to the room, you will pick two cards at random. You will win $10 if both cards are diamonds, you will win $10 if both are clubs, and for any other outcome you will lose $10. Assuming that there is no cheating, should you accept this proposition? Support your answer by calculating your probability of winning $10.