We throw 4 fair coins simultaneously and we repeat the experiment once more. What is the probability that the second throw will result in the same configuration as the first throw when the coins are indistinguishable.
Give your answer to 3 decimal places.
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I think this is simply
∑ n = 0 4 ⎝ ⎜ ⎜ ⎛ 1 6 ( x 4 ) ⎠ ⎟ ⎟ ⎞ 2 = 1 2 8 3 5
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We can look at the probability of different outcomes:
∑ p 2 = 2 5 6 1 + 1 6 + 3 6 + 1 6 + 1 = 2 5 6 7 0 = 1 2 8 3 5 ≈ 0 . 2 7 3