Conditional Probability with cards

The problem: Consider a game where 5 cards are drawn in order and then compute the following:
1. If you are told that exactly one of the first four cards drawn is Red, what is the probability that the fifth card drawn is the Ace Spades?

2. If you are told that exactly three of the first four cards drawn is Red, what is the probability that the fifth card drawn is the Ace of Spades?

Any help would be greatly appreciated. Cheers!

gainzgoblin said:

The problem: Consider a game where 5 cards are drawn in order and then compute the following:
1. If you are told that exactly one of the first four cards drawn is Red, what is the probability that the fifth card drawn is the Ace Spades?

2. If you are told that exactly three of the first four cards drawn is Red, what is the probability that the fifth card drawn is the Ace of Spades?

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Do you think that there is any difference in these two questions? Think carefully about your answer.

If we deal out twelve cards.Is there any difference in the probability that the ace of spades is the first card or the eighth card?

pka said:

Do you think that there is any difference in these two questions? Think carefully about your answer.

If we deal out twelve cards.Is there any difference in the probability that the ace of spades is the first card or the eighth card?

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These problems involve dealing out 5 cards WITHOUT REPLACEMENT. Since you are told that there are exactly X number of red cards in the first four, it does alter the probability of the final card being the ace of spades. I am just unsure of how to do the counting in this case.

gainzgoblin said:

These problems involve dealing out 5 cards WITHOUT REPLACEMENT. Since you are told that there are exactly X number of red cards in the first four, it does alter the probability of the final card being the ace of spades. I am just unsure of how to do the counting in this case.

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That is nonsense. If four cards are dealt, three red and a black, then it is given that it contains exactly one black card. By symmetry that means that it contains exactly three red cards. In either case, it does not effect the probability that the next card is the ace of spades. There is a good discussion of the problem of symmetry in the textbook Probability by Jim Pitman. It is omitted in many texts because it is such a counterintuitive idea.
In a ten card deal, it just does not seem right that the first card king is equally likely as the fifth card dealt is a king.