a bag contains 6white balls and 4red balls.three balls are drawn randomly
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Total no. of balls=10, red=4, white = 6
1 red and 2 white can be taken like this.
WWR or WRW orRWW
Probability of taking 1 red & 2white
=(6/10).(6/10).(4/10) + (6/10).(4/10).(6/10) +
(4/10).(6/10).(6/10.
=3×(6/10)×(6/10)×(4/10)
=432/1000 = .432
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Sandeep Dayananda
Sandeep Dayananda, Machine Learning Enthusiast
Answered Feb 23
As all events are independent of each other,
Final probability P(A) can be given by,
P(A) = Probability( First ball being White ) * Probability( Second ball being White ) * Probability( Third ball being Red )
= (6/10) * (6/10) * (4*10)
= 0.6 * 0.6 * 0.4
P(A) = 0.144
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Medikonda Pavan
Medikonda Pavan, studies Masters of Management at Shailesh J Mehta School Of Management, IIT Bombay (2019)
Answered Apr 7
With Replacement:
Compare this with numbers as below.
If somebody asks us find out number of three digit numbers that are possible( considering ‘000’ as a three digit number)then it would be
number of possibilities for unit digit are 10
number of possibilities for 10th digit are 10
number of possibilities for 100th digit are 10
So total number of possibilities are 10*10*10 = 1000
Now let’s say , if some body asks us form a three digit number in such a way that two digits should be from 1 - 6 and one digit would be one of 7,8,9,0. Then
one digit from 1–6 can be selected in 6 ways
and other digit from 1–6 can be selected in 6 ways
and finally another digit from 7,8,9,0 can be selected in 4 ways
and these are 6*6*4 ways
Now we have got two digits from 1–6 group and the other from (7,8,9,0) group.Consider digit of group 1–6 as ‘W’ and the other as ‘R’ then we can arrange them as
WWR, WRW, RWW in three ways.
Therefore total ways are 3*6*6*4
i.e 432
isn’t this same as drawing two whites and one red..indeed it is!
So the probability of drawing two whites and one red id 432/1000
Hope this helps!
Arindam Biswas
The bag contains 10 balls in total. So, any person can draw three balls from the bag with replacement in 1000 (10*10*10) ways. that’s your denominator. now out of these 1000 cases 2 white balls can be drawn (with replacement) in 36 (6*6) ways ( there are only 6 white balls), and for each of these 36 choices one red ball (out of 4) can be drawn in 4 ways. So, the total number of choices that are favorable here is 36*4 = 144. That’s the numerator. So, by Classical definition of probability, the answer should be 144/1000 or 0.144 . :)
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