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Aabha Mall
Asked: 2022-11-04T18:59:39+05:30 In:

A pack of cards consists of 15 cards numbered 1 to 15. Three cards are drawn at random with replacement. Then, the probability of getting 2odd and one even numbered cards is
A. `(348)/(1125)`
B. `(398)/(1125)`
C. `(448)/(1125)`
D. `(498)/(1125)`

A pack of cards consists of 15 cards numbered 1 to 15. Three cards are drawn at random with replacement. Then, the probability of getting 2odd and one even numbered cards is
A. `(348)/(1125)`
B. `(398)/(1125)`
C. `(448)/(1125)`
D. `(498)/(1125)`
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  1. Correct Answer – C
    Let `E_(i)(i=1,2,3)` denote the event of drawing an even numbered card in ith draw and `O_(i)` denote the event of drawing an odd numbered card in I th(i=1,2,3) draw. Then,
    Required probability
    `=P(E_(1) cap O_(2) O_(3)) cup (O_(1) cap E_(2) cap O_(3)) cup (O_(1) cap O_(2) cap E_(3))`
    `=P(E_(1) cap O_(2) cap O_(3))+P(O_(1) cap E_(2) cap O_(3))+P(O_(1) cap O_(2) cap E_(3))`
    `=P(E_(1))P(O_(1))P(O_(3))+P(O_(1))P(E_(2))P(O_(3))+P(O_(1))P(O_(2))P(E_(2))`
    `=(7)/(15)xx(8)/(15)xx(8)/(15)+(8)/(15)xx(7)/(15)xx(8)/(15)xx(8)/(15)xx(7)/(15)`
    `=(3xx7xx8^(2))/(15^(3))=(448)/(1125)`

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