There are 3 boxes. First box contains 4 red and 3 green, second box 3 red, 5 green and third box con

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17 Nov 2011 probability

There are 3 boxes. First box contains 4 red and 3 green, second box 3 red, 5 green and third box contains 4 red and 4 green balls. A ball has been selected and the selected ball is red. What will be the probability that the ball comes from first box.

OPtion

1) 1/81
2) 2/81
3) 12/81
4) 19/81
5) 25/36
6) 32/81
7) 40/81
8) 50/81
9) 27/100
10) 63/100

Solution

Probability = (4/7)/(4/7)+(3/8)+(4/8) = 32/81

Correct Option: 6 Best Solution (9)

madmadhav   13 years AGO

selecting red from all boxes= (4/7+3/8+1/2)
selecting from first box = 4/7

p(2nd event / 1st event)= (4/7)/(4/7+3/8+1/2)
=32/81

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Kunj Bihari   13 years AGO

prob. for 1st box= 4c1/7c1
prob. for 2nd box= 3c1/8c1
prob. for 3rd box= 4c1/8c1
hence total outcome= (4c1/7c1)+(3c1/8c1)+(4c1/8c1)
=>81/56
therefore req. prob. = (prob.1st box)/(total outcome)
=> (4c1/8c1)/(81/56)
=> 32/81

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Soni   13 years AGO

Prob of choosing red ball = 1/3 (4/7+3/8+4/8)
P(red ball is chosen from bag 1)= 1/3 * 4/7
probability that the chosen red ball comes from first box = [1/3 * 4/7]/[1/3 (4/7+3/8+4/8)] = 32/81

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Koushik Paul   13 years AGO

This problem can be done by Bayes method(URN theory).
(Prob. of getting red ball from 1st box)/(Sum of Prob. of getting red ball from 1st,2nd & 3rd box)
=(4/7)*(4/7+3/8+1/2)=(4/7)*(168/81)=32/81
So, the right option is 6) 32/81

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Honey Goel   13 years AGO

prob of red ball=1/3(4/7+3/8+1/2)=27/56
prob of red from box 1=1/3x4/7=4/21
prob that it was from box 1=(4/21)/(27/56)=32/81

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Manoj Kumar Velamala   13 years AGO

Probability of getting red from the first box =
( No. of red in first box/ Total no. in first box ) / ( No. of red in first box/ Total no. in first box + No. of red in second box/ Total no. in second box + No. of red in third box/ Total no. in third box )
Therefore probability = (4/7)/(4/7+3/8+4/8)
= 32/81

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Anish Philip   13 years AGO

4/7 * 7/23
----------
11/23
=4/11 ~ 32/81

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KOUSIK DHARA   13 years AGO

probability of red ball in 1st box / sum probability of all box of red ball=32/81

Like? Yes (1) | No (4)  

Shubham   13 years AGO

(4/7)/(4/7 + 3/8 + 1/2)

Like? Yes (1) | No (5)