Probability
Bayes theorem with biased coin
nta_pyq_2025_apr
Grade 12
Question:
A bag contains 19 unbiased coins and one coin with head$o_n$both sides. One coin drawn at random is tossed and head turns up. If the probability that the drawn coin was unbiased, is , then$n - m$is equal to m 2 2 , gcd(m,$n) = 1$n :
Step-by-Step Solution
Key Concept: Use Bayes theorem for bayes theorem with biased coin by writing the required posterior probability as a ratio of favourable conditional probabilities.
(1) 19 1 $\times$ 20 2 19 Required probability = = 19 1 1 21 $\times$ + $\times$ 1 20 2 20 m 19 ∴ = n 21 2 2 $\Rightarrow$$n - m = 441 - 361 = 80$
Correct Answer: 1