The probability of three persons A, B and C becoming clerks of a certain administrative office are 3 ∶ 2 ∶ 4. The probabilities that incentive will be introduced if they become clerks are 0.4, 0.5 and 0.3, respectively. If the incentive has been introduced, then what is the probability that C is appointed as the clerk?

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AAI ATC Junior Executive 27 July 2022 Shift 2 Official Paper
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Explanation:

Let the events be described as below:

A: The incentive has been introduced

E1: Person A appointed as the clerk

E2: Person B appointed as the clerk

E3: Person C appointed as the clerk

The probability of three persons A, B, and C becoming clerks of a certain administrative office are 3 ∶ 2 ∶ 4.

Hence, 

The probabilities that incentive will be introduced if they become clerks are 0.4, 0.5, and 0.3, respectively.

Hence, 

∴ 

∴ the required probability is

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