Consider two events T and S. Let \(\overline T\) denote the complement of the…
2024
Consider two events T and S. Let \(\overline T\) denote the complement of the event T. The probability associated with different events are given as follows:
\(𝑃(\overline T) = 0.6, 𝑃(𝑆|𝑇) = 0.3, 𝑃(𝑆|\overline T) = 0.6\)
Then, 𝑃(𝑇|𝑆) is ______ (rounded off to two decimal places).
Attempted by 4 students.
Show answer & explanation
Correct answer: 0.25
Answer: 0.25 (rounded to two decimal places)
Explanation using Bayes' theorem:
Compute P(T) from the complement: P(T) = 1 - P(overline T) = 1 - 0.6 = 0.4.
Compute P(S) by the law of total probability: P(S) = P(S|T)P(T) + P(S|overline T)P(overline T) = 0.3*0.4 + 0.6*0.6 = 0.12 + 0.36 = 0.48.
Apply Bayes' theorem: P(T|S) = P(S|T)P(T) / P(S) = 0.12 / 0.48 = 0.25.
Final result: 0.25.