# Probability of flipped coin

A bag has 3 coins a, b and c with probability of heads 0.9, 0.6 and 0.5. I flip a randomly drawn coin and get heads. What is the probability that it will come up heads again once re-flipped ?

• I don't understand how to solve it. Should the proba of what happened (head) be taken into account? – astudentofmaths Oct 23 '17 at 16:11
• Yes. This is an exercise in conditional probability. – MMASRP63 Oct 23 '17 at 16:14

probability of coin being 'a' is $\frac{0.9}{0.9+0.6+0.5}$ = 0.45

probability of heads in next turn = 0.9

.

probability of coin being 'b' is $\frac{0.6}{0.9+0.6+0.5}$ = 0.3

probability of heads in next turn = 0.6

.

probability of coin being 'c' is $\frac{0.5}{0.9+0.6+0.5}$ = 0.25

probability of heads in next turn = 0.5

Total probability = (0.45*0.9)+(0.3*0.6)+(0.25*0.5) = 0.71 \begin{align} Ans = \bbox[yellow,5px,border:2px solid red]{0.71} \end{align}

• The probability of coin being 'a' is $\frac{1}{3}$. The probability of coin 'a' will be head $0.9$ – Hasan Heydari Oct 23 '17 at 16:51
• @HasanHeydari No, your answer is wrong and this one is correct. Having flipped the coin, we have learned information about it. – David K Oct 23 '17 at 16:52