Suppose you have three coins in a bag with probabilities of heads bring 0.5, 0.6 and 0.4 respectively. A coin is picked at random and tossed until it shows up head. Find the probability that the coin is fair, if the first heads appears in the fifth toss.

Answer:[tex]\frac{1}{96}[/tex]Step-by-step explanation:Given three bags with Probabilities of heads bring is 0.5,0.6 and 0.4A coin is randomly Picked and tossed until heads AppearsProbability of choosing a fair coin is [tex]P_1=\frac{1}{3}[/tex]because coin with Probability of getting head 0.5 is fair oneProbability of getting head at 5 th toss is [tex]P_2=\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}=\frac{1}{2^5}[/tex]Thus Probability that the coin is fair, if the first head appears on 5 th tossis given by [tex]P=P_1\times P_2[/tex][tex]P=\frac{1}{3}\times \frac{1}{2^5}=\frac{1}{96}[/tex]