Multiple choice

A bag contains $n+1$ coins. It is known that one of these coins has a head on both sides while the other coins are fair. One coins is selected at random and tossed. If head turns up, the probability that the selected coin was fair, is $\displaystyle \frac { n }{ n+2 } $

  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

  2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

  3. Assertion is correct but Reason is incorrect

  4. Assertion is incorrect but Reason is correct

Reveal answer Fill a bubble to check yourself
A Correct answer
AI explanation

We must find the probability that a fair coin was chosen given that a head appeared using Bayes' theorem. The total probability of getting a head is the sum of the probability of choosing a fair coin and getting a head, which is (n/(n+1)) times (1/2), and the probability of choosing the biased coin and getting a head, which is 1/(n+1). This sum simplifies to (n+2) divided by (2n+2). Dividing the probability of a fair coin yielding a head, n/(n+1) times 1/2, by this total probability gives n/(n+2), which proves the assertion is true. Since Bayes' theorem is the fundamental rule for calculating such reversed conditional probabilities, it is the correct explanation for the assertion.