Question

1st coin 2nd coin 3rd coin outcomes
h - - - - (h,h,h)
t - - - - x
h - - - - (h,t,h)
t - - - - (h,t,t)
h - - - - (t,h,h)
t - - - - (t,h,t)
h - - - - (t,t,h)
t - - - - (t,t,t)
which outcome is represented by x?
heads on the first coin, heads on the second coin, and tails on the third coin
heads on the first coin, tails on the second coin, and tails on the third coin
heads on the first coin, heads on the second coin, and heads on the third coin
heads on the first coin, tails on the second coin, and heads on the third coin

Explanation:

Step1: Analyze the tree - diagram structure

The first coin is heads (H), the second coin is heads (H), and we are looking at the third - coin outcome for the position of x.

Step2: Determine the outcome for x

Since the first two coins are heads and for the position of x the third - coin is tails (T), the outcome is (H,H,T). This means heads on the first coin, heads on the second coin, and tails on the third coin.

Answer:

heads on the first coin, heads on the second coin, and tails on the third coin