Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

100 coins with two sides (head and tail)
20 coins are fair (50% of getting head and 50% of getting tail)
80 coins are biased (70% of getting head and 30% of getting tail)

What is the probability of get head if we throw a randomly chosen coin from the 100 coins once I said .2*.5 + .8*.7 = .66

Now, given that we got a head, what is the conditional probability that the coin we threw was biased? This is tricky for me as to how to set it up. I understand that the formula is P(A|B) = P(A intersect B)/ P(B)

but im not sure how to get P(A intersect B) or P(B) or how to assign those

share|improve this question

1 Answer 1

up vote 1 down vote accepted

Let $A$ be the event that you the coin you chose is biased and $B$ the event that the coin shows heads. Then $A\cap B$ is the event that your chosen coin is biased and shows heads, i.e. $\mathbb{P}(A\cap B) = 0.8 * 0.7$ and, as you correctly calculated, $\mathbb{P}(B) = 0.66$. Therefore $\mathbb{P}(A|B) = \frac{\mathbb{P}(A\cap B)}{\mathbb{P}(B)} \approx 0.85.$

share|improve this answer
    
very clear! thank you –  antz Nov 14 '12 at 3:47

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.