# There are two coins. One is two headed coin, the other one is a fair coin. A coin is selected randomly and flipped. a) what is the probability of selecting a fair coin? b) what is the probability of head from the flipped coin? c) what is the probability of selecting a fair coin and having head on the top?

Aarav Atkins 2022-10-22 Answered
Tossing 2 Coins, Fair coin and a two headed coin
There are two coins. One is two headed coin, the other one is a fair coin. A coin is selected randomly and flipped.
a) what is the probability of selecting a fair coin?
b) what is the probability of head from the flipped coin?
c) what is the probability of selecting a fair coin and having head on the top?
So A and B are relatively simple, because A is 1/2 and for B its 3/4 but I am concerned with C
Shouldn't be the chance of having a fair coin + head is basically 1/4? Correct me if I am wrong but
If I want to pick a fair coin, the probability is 0.5, lets say we picked it, and now we are going to throw it, isn't also chance between head and tail is 0.5? Which effectively means that getting a head from a fair coin
the intersection between them is $0.5×0.5$ which equals 0.25?
You can still ask an expert for help

## Want to know more about Probability?

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

scranna0o
Step 1
Let $F=$ "select a fair coin", and $H=$ "appear head on top"
Step 2
$P\left(F\cap H\right)=P\left(H|F\right)\cdot P\left(F\right)=\frac{1}{2}\cdot \frac{1}{2}=\frac{1}{4}$