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## Homework Statement

There is a group of four blood donors: A, B, C and D. Only A has type

A+ blood. Four blood samples, one from each individual, will be typed in random order until an A+ individual is identified. Let Y = {number of typings necessary to identify an A+ individual}. Compute the probability mass function.

## Homework Equations

permutation (order matters): n! / (n - k)!

## The Attempt at a Solution

let p = probability

p(Y=1) = 1/4

p(Y=2) = permute (1,1) * permute (1,3) / permute (2,4) = 1/4

p(Y=3) = permute (1,1) * permute (2,3) / permute (3,4) = 1/4

p(Y=4) = permute (1,1) * permute (3,3) / permute (4,4) = 1/4

Even though I think the specific order matters, it doesn't make sense that they each have a probability of 1/4. Did I miss something from the problem? Does this seem right/logical?