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Question

A box B1 contains 1white balls, 3 red balls and 2 black balls.

Another box B2 contains 2 white balls, 3 red balls and 4 black balls.

A third box B3 contains 3 white balls, 4 red balls and 5 black balls.

If 1 ball is drawn from each of the boxes B1,B2 and B3,the probability that all 3 drawn balls are of the same color, is


A

82648

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B

90648

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C

558648

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D

566648

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Solution

The correct option is A

82648


The explanation for the correct option:

Step 1: Express the given data:

In Box B1:

Number of a white ball =1

Number of red balls =3

Number of black balls =2

Therefore, total balls in bag B1=1+3+2=6

In Box B2:

Number of a white ball =2

Number of red balls =3

Number of black balls =4

Therefore, total balls in bag B2=2+3+4=9

In Box B3:

Number of a white ball =3

Number of red balls =4

Number of black balls =5

Therefore, total balls in bag B3=3+4+5=12

Step 2: Finding the probability:

The probability that it is white in all the boxes, P (All are white) =16×29×312

=6648

The probability that it is red in all the boxes, P(All are red) =36×39×412

=36648
The probability that it is black in all the boxes, P(All are black) =26×49×512

=40648

Thus the probability that all the three balls are drawn are of the same color is

=6648+36648+40648=82648

Hence, option (A) is the correct answer.


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