Comprehension

Consider the following for the two (02) items that follow:
The probabilities that A, B and C become managers are 3/10 1/2 and 4/5 respectively. The probabilities that bonus scheme will be introduced if A, B and C become managers are 4/9, 2/9 and 1/3 respectively.

What is the probability that the bonus scheme will be introduced?

This question was previously asked in
NDA-I (Mathematics) Official Paper (Held On: 13 Apr, 2025)
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  1. 17/45
  2. 19/45
  3. 23/45
  4. 26/45

Answer (Detailed Solution Below)

Option 3 : 23/45
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Detailed Solution

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Calculation:

Given,

The probability that A , B , and C  become managers are:

The conditional probabilities that the bonus scheme is introduced are:

The total probability that the bonus scheme will be introduced is given by:

Substituting the values:

Now, simplifying the terms:

The least common denominator (LCD) is 90. So:

Adding the fractions gives:

Hence, the correct answer is Option 3.

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