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 Performance Probe (Posted on 2014-10-24)
Four friends Abe, Ben, Cade and Dan sang a quartet. Two of them sang tenor, one sang baritone and one sang bass, not necessarily in that order.

It is also known that:

(i) If Ben was not one of the tenors, then Abe was the baritone.
(ii) If Dan was the baritone, then Cade was the bass.

Determine the probability that:

(a) Ben was a tenor.
(b) Abe was the baritone.

 No Solution Yet Submitted by K Sengupta No Rating

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 solution- 4 classes Comment 2 of 2 |

Let us denote the duet of tenors by T, the baritone by BR and the bass by BS.

Out of the six possible couples for  T only four are  complying with if not B then A must be BR:

AB, BC, BD, CD.

Now append each couple by BR ,then BS:

AB,C,D
AB,D,C

BC,A,D     (BC,D,A not complying with if D=BR THEN C=BS)

BD,A,C
BD,C,A

CD,A,B ……(CDBA  not complying with if not B then A= BR)….

Looking at the above listing  column-wise:

P(a)=5/6,    P(b)=3/6=1/2,    P(c)=2/6=1/3.

 Posted by Ady TZIDON on 2014-10-26 04:18:34

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