Drawn draws 1 card, replaces it, and draws another card. is it more likely that she draws 2 red cards or 2 face cards

It is more likely she will draw 2 red cards.

26 out of 52 cards in a deck are red, and 12 out of 52 cards are face cards, not including aces.

Simplify these to get 1/2 and 3/13.

Let’s find the probability for each by bringing each fraction to the power of two. This gives us 1/4 and 9/169.

The least common denominator of these two fractions is 676, giving us 169/676 and 36/676. There is a clear answer here, and that is that 169/676 (drawing 2 red cards) is more likely.

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