Consider the random permutations of [1 ... 6]. Let A be the event that the number in the first position of such a random permutation is 6, and let B be the event that the number in the last position of such a random permutation is 1. Calculate Pr[A | B].

Question

Mathematics

Rachael Solomon

12 February, 08:20

Consider the random permutations of [1 ... 6]. Let A be the event that the number in the first position of such a random permutation is 6, and let B be the event that the number in the last position of such a random permutation is 1. Calculate Pr[A | B].

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Answers (1)

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Tristan Leon · Answer 1

Pr[A | B] = 0.2

Step-by-step explanation:

If we have a permutation of {1,2,3,4,5,6} that ends in 1, then we will have only 5 possibilities for the first spot, 2,3,4,5 and 6. All of them equally probable. Thus, the probability that in the first position of a random permutation there is a 6, giving that in the last position there is a 1 is 1/5 = 0.2