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Pat and Sam are arguing about the probability of obtaining 2 heads and 2 tails in 4 flips of a fair coin, in that specific order. Pat says, "The probability equals 1/16, since there is one way this outcome can occur, and the experiment has 16 different possible outcomes". Sam says "The probability equals 6/16, since the corresponding entry in row 4 of Pascal's triangle is 6, and the sum of the entries in that row equals 16." Who is correct, and why?

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Answer:

Pat's right, because there are no permutations.

Step-by-step explanation:

Since there is a specific order, there are no permutations. The relationship between the binomial distribution and Pascal's triangle happens when there are permutations.

So, the correct logic is Pat's.

Each flip has 0.5 probability of having the desired result. There are four flips. So:

[tex]P = (0.5)^{4} = \frac{1}{2}^{4} = \frac{1}{16}[/tex].

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