If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Course: Class 12 math (India) > Unit 15

Lesson 2: Bayes' theorem
Math
Class 12 math (India)
Probability
Bayes' theorem
© 2024 Khan AcademyTerms of usePrivacy PolicyCookie Notice

Theorem of total probability

Google Classroom

Problem

Three cities X, Y and Z suffer from high levels of pollution.
The probabilities that the pollution level is "severe" are 0.4, 0.3 and 0.9 for cities X, Y and Z respectively.
A city is chosen at random and its pollution level measured.
Find the probability that the measured pollution level is "severe".
Express your answer as a number, rounded to two decimal places.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi