Finite fair and unfair coins

Question

You have two coins. One is fair and the other is unfair with the probability of heads being 0.6. First the fair coin is flipped with the outcome being recorded.

If the result is tails, then the same fair coin is flipped with the outcome recorded.
If the result is heads, then the unfair coin is flipped with the outcome recorded.
What is the probability of getting at least 1 tails?

Answer 1

Drawing a tree diagram might help, but that's hard to do here, so we'll just look at the options.

 

You could get HH, HT, TH, or TT.  Only one of those doesn't have a tails.  So we can find the chance of that happening and then think about the opposite of it.

 

To get HH, you have a .5 chance and then a .6 chance so that would be (.5)(.6) = .30  (or 30%)

So the probability of getting at least 1 tails would be .70, or a 70% chance.

 

 

You could also find the chance of the three events with tails happening and then add them up.

 

HT = (.5)(.4) = .20  (had to flip unfair coin)

TH = (.5)(.5) = .25

TT = (.5)(.5) = .25

 

.25 + .25 + .20 = .70