NTA Test 13 (Numerical)
The minimum number of times a fair coin needs to be tossed, so that the probability of getting at least two heads is at least 0%, is
Step-by-Step Solution
Key Concept: Apply Bayes' theorem to find posterior probability of selecting a machine given a defective unit
Given $P(T_i) = \frac{25}{100}$ and $P(T_j) = \frac{35}{100}$, and $P\left(\frac{D}{i}\right) = 2$ (where $D$ represents defective units), we find $P\left(\frac{i}{D}\right) = 10x$. Using Bayes' theorem with $P(D) = \frac{30}{100}$ (given), we compute: $\frac{25}{100} \times 10x + \frac{35}{100} \times x = \frac{30}{100}$, solving to get $x = \frac{10}{285}$, thus $P\left(T_j|D\right) = \frac{35}{100} \times \frac{10}{285} = \frac{7}{57}$.
Correct Answer: C