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A box contains 24 identical balls of which 12 are black and 12 are white.The balls are drawn at random from the box one at a time with replacement.The probability that a white ball is drawn for the fourth time on the seventh draw is Ans=> 5/32 Please explain how this answer came. The explanation should be detailed as i have found this question on many books also but not understood.

A box contains 24 identical balls of which 12 are black and 12 are white.The balls are drawn at random  from the box one at a time with replacement.The probability that a white ball is drawn for the fourth time on the seventh draw is


Ans=> 5/32


Please explain how this answer came.


The explanation should be detailed as i have found this question on many books also but not understood.

Grade:12th Pass

1 Answers

arpan chandrashekhar
5 Points
10 years ago

think of it this way:

the fourth draw is gonna happen at the 7th draw...

this means 3 draws have already occured in the previous 6

this means it COULD HAVE OCCURED IN 6C3 ways= 20 ways

and total ways or possibilites(sample space) for that was 2^6 (because the are only 2 colours and either white or black, ie 1+1=2 and 6draws therefore 2^6)

"AND"the seventh ball would be white has probability 12/24 = 1/2...

so total probability is

(20/2^6)*(1/2) =5/32

i hope u understood :)

if u dint feel free to ask again

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