Rachel and her little sister Christie often argue about who should wash the dishes at their house. Rachel suggests that they flip coins to solve their argument.
"Flipping a coin is fair, since heads and tails each have an equal chance of happening.
Each one has a probability of " Rachel says. "If the coin shows heads, then I do the
dishes. If it shows tails, then you do them."
a. Is this system fair? That is, does each girl have an equal likelihood of washing the
dishes each day? What is the theoretical probability for heads? For tails?
b. Rachel and Christie flip a coin every evening for the first week. Christie has washed
the dishes four times, and Rachel has washed the dishes three times. Christie tells
Rachel that the system is not fair, because Christie has done the dishes more often
than Rachel. Is Christie right?
c. After the second week of coin flipping, Christie has washed the dishes ten times and
Rachel has washed the dishes four times. Now Christie is really upset at Rachel
because she has washed the dishes so many times.
In light of this new information, do you think the system is fair or not fair? What
would you recommend to Christie?