You are expecting two sets of exams- “easy” and “hard”. The probability of getting a hard exam is 0.80. The probability that the first question on the exam will be difficult is 0.90 if the set is “hard” and is 0.15 if the set is “easy. a) What is the probability that the first question on your exam is marked as difficult. b) What is the probability that your exam is hard given that the first question on the exam is marked as difficult?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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You are expecting two sets of exams- “easy” and “hard”. The probability of getting a hard exam is 0.80. The probability that the first question on the exam will be difficult is 0.90 if the set is “hard” and is 0.15 if the set is “easy.

  1. a) What is the probability that the first question on your exam is marked as difficult.
  2. b) What is the probability that your exam is hard given that the first question on the exam is marked as difficult?
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