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.

(c) Cade was the bass.

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.**