Question

a bag contains two coins ,one biased and the other unbiased.when tossed the biased coin has a 60% chances of shoeing heads.One of the coins is selected at random and on tossing it shows tails . what is the probability it was an unbiased coin?

Answer 1

Answer:

it will be 50% of chance

Step-by-step explanation:

No. of favourable outcomes(unbiased coin)= 1

No. of total outcomes = 2( 1 biased coin and 1 unbiased coin)

probability = 1/2

= 50%

Answer 2

The probability that heads shows up on a unbiased coin is equal to 5/11.

Let E - event that head shows up on a coin.

E1 - event that biased coin is chosen .

E2 - event that unbiased coin is chosen.

P(E1) = 1/2 and P(E2) = 1/2

P(E/E1) = 3/5 and P(E/E2) = 1/2

P(E2/E) = the probability that the heads shows up on the unbiased coin

Using Bayes theorem to find the probability -

P(E2/E) = P(E2)P(E/E2)/(P(E2)P(E/E2)+P(E1)P(E/E1))

= (1/4)/((1/4)+(3/10))

= 5/11