Question

A friend makes three pancakes for breakfast. One of the pancakes is burned on both sides, one is burned on only one side, and the other is not burned on either side. You are served one of the pancakes at random, and the side facing you is burned. What is the probability that the other side is burned? (Hint: Use conditional probability.)

Enter the exact answer.

**The answer is NOT 0.5 or 1/2, when I put either of those, it says it is incorrect.**

Answer 1

A friend makes three pancakes for breakfast. one of the cakes is burnt on both sides, one is burnt on one side, and the other is not burnt on either side.

One cake is served at random, and the side facing is burnt.

To find the chance that the other side is burnt.

ie. to find P(other side is burnt|facing side is burnt)

=P(one side is burnt and other side is burnt)/P(facing side is burnt)

=P(both sides burnt)/P(facing side burnt)

Now,

By total probability theorem,

P(facing side is burnt)

=P(first cake)P(facing side burnt|first cake)+P(second cake)P(facing side burnt|second cake)+P(third cake)P(facing side burnt|third cake)

=(1/3)*(1+0.5+0)

=1.5/3

=0.5

And, P(both sides burnt)

=1/3

as there are 3 cakes in total, and only one of them are burnt at both sides.

So, the required conditional probability is

=P(Both sides burnt)/P(one side burnt)

=(1/3)/(0.5)

=0.66.

Thus, the Required answer is 0.66