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Krishna Malhotra
Asked: 2022-11-09T20:43:29+05:30 In:

The probability that randomly selected calculator from a store is of brand r is proportional to r, r=1,2,..,6. Further, the probability of a calucltor of brand r being defective is `(7-r )/(21), r=1,2,..,6`. Then the probability that a calculator randomly selected from the store being defective is
A. `(8)/(63)`
B. `(13)/(63)`
C. `(55)/(63)`
D. `(50)/(63)`

The probability that randomly selected calculator from a store is of brand r is proportional to r, r=1,2,..,6. Further, the probability of a calucltor of brand r being defective is `(7-r )/(21), r=1,2,..,6`. Then the probability that a calculator randomly selected from the store being defective is
A. `(8)/(63)`
B. `(13)/(63)`
C. `(55)/(63)`
D. `(50)/(63)`
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  1. Correct Answer – A
    Let `C_(r )` denote the event that a calculator of brand r is selected and `D_(r )` denote the event that a calculate of brand r is defective. Then,
    `P(C_(r ))=lamda r ” and ” P(D_(r )//C_(r ))=(7-r)/(21), r=1, 2,..,6`.
    Now, `underset(r=1)overset(6)(sum)P(C_(r )=1`
    `implies underset(r=1)overset(6)(sum) lamda r=1 implies lamda(underset(r=1)overset(6)(sum) r)=1 implies 21 lamda =1 implies lamda =(1)/(21)`
    Required probability `= underset(r=1)overset(6)(sum) P(C_(r ) cap D_(r ))`
    `= underset(r=1)overset(6)(sum) P(C_(r ))P(D_(r )//C_(r ))`
    `= underset(r=1)overset(6)(sum) lamda r xx(7-r)/(21)`
    `=(lamda)/(21) underset(r=1)overset(6)(sum) (7r – r^(2))`
    `=(1)/(21^(2)){ underset( r=1)overset(6)(sum) 7r- underset(r=1)overset(6)(sum) r^(2)}`
    `=(1)/(21^(2)){7xx21-(6xx7xx13)/(6)}=(8)/(63)`

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