Question

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 1

Answer:$\frac{1}{96}$

Step-by-step explanation:

Given three bags with Probabilities of heads bring is 0.5,0.6 and 0.4

A coin is randomly Picked and tossed until heads Appears

Probability of choosing a fair coin is $P_1=\frac{1}{3}$

because coin with Probability of getting head 0.5 is fair one

Probability of getting head at 5 th toss is

$P_2=\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}=\frac{1}{2^5}$

Thus Probability that the coin is fair, if the first head appears on 5 th toss

is given by

$P=P_1\times P_2$

$P=\frac{1}{3}\times \frac{1}{2^5}=\frac{1}{96}$