Tree and Venn Diagrams · Exercise 10

When the euro coin was introduced in 2002, two math professors had their statistics students test whether the Belgian one euro-coin was a fair coin. They spun the coin rather than tossing it and found that out of 250 spins, 140 showed a head (event H) while 110 showed a tail (event T). On that basis, they claimed that it is not a fair coin.

(a) Based on the given data, find P(H) and P(T).
(b) Use a tree to find the probabilities of each possible outcome for the experiment of spinning the coin twice.
(c) Use the tree to find the probability of obtaining exactly one head in two spins of the coin.
(d) Use the tree to find the probability of obtaining at least one head.

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Statistics · §3.5 Tree and Venn Diagrams · Exercise 10