## A yes/no test

Posted by Chris on October 17, 2014 – 10:21 am

In a test involving yes/no answers, the probability that the official answer is correct is t, the probability of getting the real correct answer is b for a boy and g for a girl. If the probability that a randomly chosen boy or girl of getting the official answer to a question is 1/2, then what is the ratio of boys to girls who took the test?

October 20th, 2014 at 5:28 am

(0.5-g)/(b-0.5)

October 21st, 2014 at 10:04 am

~~Hi jan. You’ve made a small slip somewhere. But you are nearly right.~~EDIT: I had calculated B/(B+G) instead of B/G. So jan was right.

October 22nd, 2014 at 7:26 am

I don’t get it. If b=0.6 and g=0.2 then 0.3/0.1=3. Which means that there are 3 boys for each girl.

October 22nd, 2014 at 3:44 pm

Hi jan. I’ve just noticed that I made the slip, not you.

b = 0.6 and g = 0.2 => B/G = 3. That seems fine to me.

Note that because the overall probability of picking a child at random and of them agreeing with the official test answer is 0.5, there are restrictions on the possible simultaneous values of b and g.

The possibly unexpected result is that B/G is independent of the probability of the official test answer, t, being correct.

October 27th, 2014 at 5:38 am

“The possibly unexpected result is that B/G is independent of the probability of the official test answer, t, being correct.”

Could you please elaborate on this. I don’t understand what this means.

October 27th, 2014 at 11:33 am

Hi jan. t doesn’t appear in the expression for B/G, so there was no need for it to be included in the problem.