Question

A box contains three coins: two regular and one fake one-sided coin (P(H) = 1) You pick a coin at random and toss it. What is the probability that it lands tails up? You pick a random coin and after tossing get H. What is the probability that the coin is not fake?

Answer 1

0.50

Explanation:

Given that a box contains three coins: two regular and one fake one-sided coin (P(H) = 1) You pick a coin at random and toss it.

Probability of selecting any one coin = 1/3

The coins are regular 1, regular 2 , fake

P for head 0.5 0.5 1

Probability for head =
`(1)/(3) (1+0.5+0.5) = 0.6667`

using total probability theorem for mutually exclusive and exhaustive)

Probability that coin is not fake/head =
`(0.5+0.5)/(1+0.5+0.5) \\= 0.5`