Aptitude - Probability - Discussion

@ : Home > Aptitude > Probability > General Questions - Discussion

"Act well your part; there all honor lies."

- Alexander Pope

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:

[A].

[B].

117

[C].

[D].

Answer: Option B

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

Prabhu said: (Fri, May 13, 2011 09:50:35 AM)

(10C1 x 15C2) why they are multiplying this ? They should add the value know .. 10 c1 + 15 c2

Priya said: (Fri, May 20, 2011 02:47:48 AM)

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

Gnana said: (Mon, May 23, 2011 11:08:08 AM)

I too have same doubt. Can any one clarify this, soon.

Mahesh Babu said: (Fri, Jun 17, 2011 08:57:29 AM)

Because he asked 10 girls (and) 15 boys.

Sanjana said: (Sun, Jun 26, 2011 02:56:36 PM)

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 ""

Abhi said: (Mon, Aug 29, 2011 12:45:12 PM)

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: (Wed, Sep 28, 2011 04:12:23 PM)

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.

Al Ford said: (Thu, Nov 10, 2011 05:21:42 AM)

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?