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.

Accepted Solution

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]