Aptitude - Probability - Discussion

Discussion Forum : Probability - General Questions (Q.No. 7)
7.
In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:
21
46
25
117
1
50
3
25
Answer: Option
Explanation:

Let S be the sample space and E be the event of selecting 1 girl and 2 boys.

Then, n(S) = Number ways of selecting 3 students out of 25
= 25C3 `
= (25 x 24 x 23)
(3 x 2 x 1)
= 2300.

n(E) = (10C1 x 15C2)
= 10 x (15 x 14)
(2 x 1)
= 1050.

P(E) = n(E) = 1050 = 21 .
n(S) 2300 46

Discussion:
54 comments Page 1 of 6.

Prabhu said:   1 decade ago
(10C1 x 15C2) why they are multiplying this ?

They should add the value know .. 10 c1 + 15 c2

Priya said:   1 decade ago
@prabhu.

Even I have the same doubt. Can some intellectual person answer this?

Gnana said:   1 decade ago
I too have same doubt. Can any one clarify this, soon.

Mahesh babu said:   1 decade ago
Because he asked 10 girls (and) 15 boys.

Sanjana said:   1 decade ago
If they ask for same collections for example (a bag contains 6 white and 4 black balls.two balls are drawn at random.find the probability that they are of same color) here they are askin for same color in this case we have to use "+" i.e, 6c2+4c2

but here in a above problem they have tld us to select 1 girl out of 10 girls and 2 boys out of 15 boys.and here its not of same combination they are askin for both boy and gal.in this case we have to use "*" i.e, 10C1 x 15C2

Note tat: if its same color or combination go for "+"
If its different combination go for "*"

Prabhat said:   1 decade ago
Nice explanation sanjana.

Abhi said:   1 decade ago
I solved this problem as
(10/25)*(15/24)*(14/23)

because 1st select 1 girl from 10 out of total 25 students, then 1 boy from 15 out of remaining 24 then again 1 boy from 14 boys and total remainig 23 students.... i got 7/46 as my ans.....

Can anyone please tell me whats wrong? please..

Kruvy said:   1 decade ago
You got the Point @Abhi .. :-)

However I cannot help you in this. As I have no clue about is this a right method and robust to solve same kind of problem...??!

Help us.

And I Like this site. Appreciate it @IndiaBix.

Swetha said:   1 decade ago
Thanks sanjana.

Al Ford said:   1 decade ago
I have a similar problem. Can anyone explain how to answer this: A class contains 7 women and 7 men. Suppose we choose three random students. How many ways can we choose exactly 1 woman?


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