Background,

Here in Europe, we have tv adverts that come up with statements on lines of

When advertising things like hair products, "65 % of women agreed" , to a question like "my hair is shinier than the other product"

At the bottom in small print , they have to show the sample size,

which in this case was 43 of 67 agree.

Now ignoring the the fact the that should be 64%, i.e. they have rounded up.

It got me wondering,

and I know we have some great mathematicians here,

If lets say, the odds of a person agreeing is 50:50

How many would we have to ask, to have a 50:50 chance of finding a run of 67 where 43 agree ?