We are given three coins: one has heads in both faces, the second has tails in both faces, and the third has a head in one face and a tail in the other. we choose a coin at random, toss it, and it comes head. what is the probability that the opposite face is tails?

0.33

Step-by-step explanation:

Let,

In this question we are using the Bayes' theorem,

where,

P(E1) = P(E2) = P(E3) =

As there is an equal probability assign for choosing a coin.

Given that,

it comes up heads

so, let A be the event that heads occurs

then,

P(A/E1) = 1

P(A/E2) = 0

P(A/E3) =  

Now, we have to calculate the probability that the opposite side of coin is tails.

that is,

P(E3/A) = ?

∴ P(E3/A) =

=

= ×

=

= 0.3333 ⇒ probability that the opposite face is tails.

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