Question

Two cards will be dealt off the top of a well-shuffled deck. You have a choice: (i) to win $1 if at least one of the two cards is queen. (ii) to win$1 if the first is a queen. Which option is better? Or are they equivalent? Explain.

Solution

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Two cards are being selected.

We win in option (i) when at least one of the cards is a queen. Thus we win in option (i) when the first card is a queen or the second card is a queen or both.

We win in option (ii) when the first card is a queen. We then note that we win in option (i) whenever we win in option (ii).

However, when only the second card is a queen, then we note that we win in option (i) but not in option (ii) and thus we have more chances of winning in option (i), which implies that option (i) is better as we are paid out the same amount in both options.

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