Question

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?

Answer 1

Answer: 0.33

Step-by-step explanation:

Let,

• E1 be the coin which has heads in both faces

• E2 be the coin which has tails in both faces

• E3 be the coin which has a head in one face and a tail in the other.

In this question we are using the Bayes' theorem,

where,

P(E1) = P(E2) = P(E3) = $\frac{1}{3}$

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) =  $\frac{1}{2}$

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

that is,

P(E3/A) = ?

∴ P(E3/A) = $\frac{P(E3)P(A/E3)}{P(E1)P(A/E1) + P(E2)P(A/E2) + P(E3)P(A/E3) }$

= $\frac{(1/3)(1/2)}{(1/3)(1) + 0 + (1/2)(1/3)}$

= $\frac{1}{6}$ × $\frac{6}{3}$

= $\frac{1}{3}$

= 0.3333 ⇒ probability that the opposite face is tails.