Question

You draw a coin from a collection of 4 coins. 2 are fair coins, and 2 are weighted so they land on heads 90% of the time. you cannot tell the coins apart through inspection. you choose a coin and flip it once. what is the probability that the coin lands heads up? express your answer as a decimal.

Answer 1

The coin we choose is equally likely to be fair or unfair, since the ratio of fair to unfair coins is 2:2 = 1:1.

So, 50% of the times we pick a fair coin, which lands on heads with probability 50%.

The other 50% of the times we pick an unfair coin, which lands on heads with probability 90%.

Since these two events are mutually exclusive (a coin is either fair or unfair), the probability of having the coin to land on heads is

$\underbrace{0.5\times 0.5}_{\text{fair coin lainding on heads}} + \underbrace{0.5\times 0.9}_{\text{unfair coin lainding on heads}} = 0.25 + 0.45 = 0.65$