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An instructor has a question bank consisting of 300 easy True / False questions,200 difficult True / False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question?
  • a)
    7/9
  • b)
    5/9
  • c)
    1/9
  • d)
    4/9
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
An instructor has a question bank consisting of 300 easy True / False ...

Total = 1400, therefore n(S) = 1400 Let A = event of getting easy question B = event of getting multiple choice question.
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Most Upvoted Answer
An instructor has a question bank consisting of 300 easy True / False ...
Given:
- 300 easy True / False questions
- 200 difficult True / False questions
- 500 easy multiple choice questions
- 400 difficult multiple choice questions

To find:
- Probability of selecting an easy question given that it is a multiple choice question

Solution:
Total number of questions = 300 + 200 + 500 + 400 = 1400
Total number of multiple choice questions = 500 + 400 = 900
Total number of easy multiple choice questions = 500

The probability of selecting an easy multiple choice question can be found using the conditional probability formula:

P(Easy | Multiple choice) = P(Easy and Multiple choice) / P(Multiple choice)

P(Easy and Multiple choice) = 500 / 1400 = 5/14
P(Multiple choice) = 900 / 1400 = 9/14

Putting the values in the formula, we get:

P(Easy | Multiple choice) = (5/14) / (9/14) = 5/9

Therefore, the probability of selecting an easy question given that it is a multiple choice question is 5/9.

Answer: (b) 5/9
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An instructor has a question bank consisting of 300 easy True / False questions,200 difficult True / False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question?a)7/9b)5/9c)1/9d)4/9Correct answer is option 'B'. Can you explain this answer?
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