The GATE Grind

GATE 2024 DA – Question 58

Probability and Statistics · Counting, probability axioms, conditional probability and Bayes theorem · 2 marks · Numerical answer

Consider two events T and S. Let $\bar{T}$ denote the complement of the event T. The probability associated with different events are given as follows: $P(\bar{T}) = 0.6$, $P(S|T) = 0.3$, $P(S|\bar{T}) = 0.6$.

Then, $P(T|S)$ is ______ (rounded off to two decimal places).

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 0.24 to 0.26

Explanation

$P(T) = 1 - 0.6 = 0.4$. By the total probability, $P(S) = 0.3 \times 0.4 + 0.6 \times 0.6 = 0.12 + 0.36 = 0.48$. By Bayes' theorem, $P(T|S) = \frac{P(S|T)P(T)}{P(S)} = \frac{0.12}{0.48} = 0.25$.