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You take eight cards - two 2's, two 3's, two 4's, and two 5's - and...

You take eight cards - two 2's, two 3's, two 4's, and two 5's - and form a deck. You shuffle the deck and randomly reveal cards one at a time until you have two that match.

What is the expected number of cards you will need to reveal to get a matching pair?

  1. 3.54

  2. 3.66

  3. 3.72

  4. 3.83

  5. 3.91

math   Statistics-And-Probability   
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Answer #1

let X be the number oif cards to be taken:

P(X=2) =P(first and 2nd both are same) =(8/8)*(1/7) =1/7

P(X=3) =P(First 2 are different and 3rd is same)=(8/8)*(6/7)*(2/6)=2/7

P(X=4)=(8*6*4*3)/(8*7*6*5)=12/35

P(X=5) =P(first 4 are different) =(8*6*4*2)/(8*7*6*5)=8/35

therefore expected cards E(x)=2*1/7+3*2/7+4*12/35+5*8/35=3.66

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