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:
`(1)/(96)`

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=(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=(1)/(2)* (1)/(2)* (1)/(2)* (1)/(2)* (1)/(2)=(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* P_2`

`P=(1)/(3)* (1)/(2^5)=(1)/(96)`