Problem Solving

The odds that Amit speaks the truth are 1:2 and the odds that Bunty speaks the truth are 2:3. What is the probability that exactly one of Amit is speaking the truth?

A. 3/5

B. 4/15

C. 7/15

D. 4/7

E. 3/7

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dtweah wrote:The odds that Amit speaks the truth are 1:2 and the odds that Bunty speaks the truth are 2:3. What is the probability that exactly one of Amit is speaking the truth?

A. 3/5

B. 4/15

C. 7/15

D. 4/7

E. 3/7

[spoiler]https://www.greguide.com/Free-GRE-Practi ... est-5.html[/spoiler]

Hi,

the wording isn't great on this question, but we can figure out what the author meant to ask, so let's answer the "spirit" of the question. I've never heard of this source before, so no clue if ambiguously worded questions are the norm.

The probability that amit is speaking the truth is 1/3; the probability that Bunty is speaking the truth is 2/5. There are two scenarios that match our desired outcome:

A true, B lie; and
A lie, B true.

Calculation each scenario:

(1/3)*(3/5) = 3/15
(2/3)*(2/5) = 4/15

Since we're happy with EITHER scenario, we ADD the probabilities:

3/15 + 4/15 = 7/15... choose C.