Answer:
a) probability of choosing heads= 1/2 (50%)
b) probability of choosing the fair coin knowing that it showed heads is= 1/3 (33.33%)
Step-by-step explanation:
Since the unfair coin can have 2 heads or 2 tails , and assuming both are equally possible . then
probability of choosing the fair coin (named A)= 1/2
probability of choosing an unfair coin with 2 heads (named B)= (1-1/2)*1/2= 1/4
probability of choosing an unfair coin with 2 tails (named C)= (1-1/2)*(1-1/2)= 1/4
then
probability of choosing heads= probability of choosing A * probability of getting heads from A + probability of choosing B * probability of getting heads from B + probability of choosing C * probability of getting heads from C =
1/2*1/2 + 1/4*1 + 1/4*0 = 2/4 = 1/2
the probability of choosing the fair coin knowing that it showed heads is
P(A/B) = P(A∩B)/P(B)
denoting event A= the coin is fair and event B= the result is heads
P(A∩B) = 1/2*1/2 = 1/4
but since we know now that that the unfair coin is not possible , the probability of choosing heads is altered:
P(B)=probability of choosing heads= probability of choosing A * probability of getting heads from A + probability of choosing B * probability of getting heads from B = 1/2*1/2+1/2*1 = 3/4
then
P(A/B) = P(A∩B)/P(B) = (1/4)/(3/4) = 1/3
then the probability is 1/3
