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For a post three person A1, A2, A3 appea...

For a post three person `A_1, A_2, A_3` appear in the interview. The probability of `A_1` being selected is twice as much as that of `A_2` and the probability of `A_2` being selected is three times as much as that of `A_3`. What are the individual probabilities of `A_1, A_2, A_3` being selected?

Text Solution

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Let `E_1, E_2, E_3` be the events of `A_1, A_2, A_3` being selected respectively.
Assume `P(E_3)=p, " them P(E_2)=3p " and " P(E_1)=6p`
There are 3 candidates, but exactly one will be selected.
`therefore P(E_1cupE_2cupE_3)=1`
`E_1, E_2, E_3` are mutually exclusive. Using this in the above equation.
`P(E_1)+P(E_2)+P(E_3)=1`
`implies 6p+3p+p=1 implies 10p=1`
`therefore " " p=1/10`
Thus `P(E_3)=1/10,P(E_2)=3/10 " and " P(E_1)=6/10=3/5`
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