Suppose you shuffle a pack of four cards-two red, two black-and deal them face d

Q: Suppose you shuffle a pack of four cards-two red, two black-and deal them face d

We have 4 cards: 2 red and 2 black. Total number of ways of picking up 2 cards = 4C2 = 6 Next, we either select 2 red cards from 2 red cards or 2 black card from 2 black cards to match: = 2C2 + 2C2 = 2 ways Hence, we can match in 2 out of 6 ways Probability = 2/6 = 1/3 = 0.33

ID: 3204927 • Letter: S

Question

Suppose you shuffle a pack of four cards-two red, two black-and deal them face down in a row. Two cards are picked at random, say by placing a penny on each. What is the probability that those two cards are the same color? One person reasons: "There are three equally probable cases. Either both cards are black, both are red, or they are different colors. In two cases, the cards match, therefore the matching probability is 2/3." "No, " another person counters, "there are four equally probable cases. Either both cards are black, both are red, card x is black and y is red, or x is red and y is black. More simply, the cards either match or they do not. In each way of putting it the matching probability clearly is 1/2. The fact is that both people are wrong. Compute the correct probability.

Explanation / Answer

We have 4 cards: 2 red and 2 black.

Total number of ways of picking up 2 cards = 4C2 = 6

Next, we either select 2 red cards from 2 red cards or 2 black card from 2 black cards to match:

= 2C2 + 2C2 = 2 ways

Hence, we can match in 2 out of 6 ways

Probability = 2/6 = 1/3 = 0.33

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Suppose you shuffle a pack of four cards-two red, two black-and deal them face d

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