Question

A high-school teacher takes an afternoon to teach their class some basic ideas about probability. They do this by getting the students to toss coins (head or tails) and set up a tournament where the 32 students split into pairs and have a contest: the students in each pair toss a coin ten times and the winner is the student who tosses the most heads.

Then the 16 students who were winners in the first round are again split into pairs to have the same contest. From this round the 8 winning students are chosen to play in the next round and so forth. At the end of the tournament, the winning student, Rebecca, has just won 5 contests of tossing heads in a row.

The teacher then asked the class what they think is going to happen if Rebecca now tosses a coin 100 times. Some students think that Rebecca will get close to 50 heads out of 100. Other students think that Rebecca is obviously very good at tossing heads and will get as many as 90 heads out of 100. Answer the following:

(a) Which group of students do you think are correct? Explain your answer.

(b) Suppose Rebecca does only toss close to 50 heads out of 100. What has gone wrong with her head throwing abilities? What is the general statistical concept that explains this type of situation? i.e. Having performed very well at something in the past doesn’t necessarily indicate excellence in the future. Explain why this concept explains Rebecca’s situation.

Answer 1