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The odds that a book will be favourable received by 3 independent received by 3 independent reviewers are 5 to 2, 4 to 3 and 4 to 4 respectively. What is the probability that out of 3 reviewers a majority will be favourable?
  • a)
    209/343
  • b)
    209/434
  • c)
    209/443
  • d)
    209/350
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The odds that a book will be favourable received by 3 independent rece...
To find the probability that a majority of the 3 reviewers will give a favorable review, we need to consider the different combinations of favorable and unfavorable reviews that can occur. Let's analyze each scenario:

1. All 3 reviewers give a favorable review:
The probability of this scenario is (5/7) * (4/7) * (4/8) = 80/343.

2. Two reviewers give a favorable review and one gives an unfavorable review:
We need to consider all possible combinations of 2 favorable and 1 unfavorable review. There are 3 ways this can happen:
- Favorable, Favorable, Unfavorable: (5/7) * (4/7) * (4/8) = 80/343
- Favorable, Unfavorable, Favorable: (5/7) * (3/7) * (4/8) = 60/343
- Unfavorable, Favorable, Favorable: (2/7) * (4/7) * (4/8) = 32/343

The total probability for this scenario is 80/343 + 60/343 + 32/343 = 172/343.

3. One reviewer gives a favorable review and two give an unfavorable review:
Again, we need to consider all possible combinations. There are 3 ways this can happen:
- Favorable, Unfavorable, Unfavorable: (5/7) * (3/7) * (4/8) = 60/343
- Unfavorable, Favorable, Unfavorable: (2/7) * (4/7) * (4/8) = 32/343
- Unfavorable, Unfavorable, Favorable: (2/7) * (3/7) * (4/8) = 24/343

The total probability for this scenario is 60/343 + 32/343 + 24/343 = 116/343.

4. All 3 reviewers give an unfavorable review:
The probability of this scenario is (2/7) * (3/7) * (4/8) = 24/343.

Adding up the probabilities for all scenarios where a majority of the reviewers give a favorable review, we get:
80/343 + 172/343 = 252/343.

Therefore, the probability that out of 3 reviewers a majority will be favorable is 252/343, which is approximately 0.734 or 73.4%. This corresponds to answer choice A: 209/343.
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