Mathematics in adolescence

Question

When I start to teach probabilities, I challenge my students with the following:

Thelma is 16 years old and can only go out at night if one of her parents gives her permission.  She knows her father is less tough then her mother (he lets her go out more often).  She also knows that if she asks permission two consecutive days at the same parent, the answer is never the same. If she asks one parent and he/she says no, Thelma can't go out that night. One weekend, Thelma wants to go out two nights in a row (on Friday and Saturday, or on Saturday and Sunday). How should Thelma proceed to optimize the chances of her parents let her do it?

"Math is great, even when you are a teenager!"

Jaap Scherphuis · Accepted Answer

Suppose Thelma asks her mother on the first day.

I originally misread the question, thinking that the rule was that if you ask one parent on two consecutive days, they won't say yes twice. This is a pretty interesting question too, so I'll keep the answer for that question below:
Clearly she must alternate which parent she asks, because if she asks the same parent twice in a row it definitely won't happen for that pair of days. So she must decide between the order mum-dad-mum or dad-mum-dad.
Before going into the maths, Thelma might intuitively think the latter is better, because the dad is more lenient and so she is likely to go out more days.

Here is the maths:
Let $m$ be the probability that mother gives permission when asked, and $d$ the same for her father. We are given that $m<d$.

Mathematics in adolescence

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