You start dealing from one deck of cards and the first card dealt is not a face card. Does that mean that the chance of the next card not being a face card is 35/51 or is it as follows: The chances that the first card will not be a face card are 36/52. Once the first card is not a face card, the chance that the second card will not be a face card also are 36/52 X 36/51 which is lower than 36/52. Why is the second answer to this question wrong?
You start dealing from one deck of cards and the first card dealt is not a face card. Does that mean that the chance of the next card not being a face card is 35/51 or is it as follows: The chances that the first card will not be a face card are 36/52. Once the first card is not a face card, the chance that the second card will not be a face card also are 36/52 X 36/51 which is lower than 36/52. Why is the second answer to this question wrong?
The second solution is an attempt to answer the question, "What is the chance that the first TWO cards will not be face cards?" The answer to this would be 36/52 x 35/51.
Once you know that first card is not a face card, however, as you stated in your original problem, "You start dealing from one deck of cards and the first card dealt is not a face card....," you no longer have to calculate the probability for the first card. In other words, since you've already stipulated that the first card is not a face card, all we're concerned with is subsequent cards. The correct answer is thus 35/51.
David
