Discussion Problem of The Day (18/06/2011)

[varsha]

---------- Forwarded message ----------
From: k varsha <[hidden email]>
Date: Sat, Jun 18, 2011 at 10:30 AM
Subject: Discussion Problem of The Day (18/06/2011)
To: [hidden email]


Suppose that 10 cards of which 5 are green and five are red, are placed at random in 10 envelopes,of which five are green and five are red.Determine the probability that exactly 'x' envelopes will contain a card with matching color ?

[Mahima]

the probability when x is odd, is zero.
when x is even, prob for x=0 and x=10 is [(5!)^2]/10!
when x=2 and x=8, prob is [(4!)^2]/10!
when x=4 and x= 6, prob is [(3!)^2 *2*2]/10!

please confirm!

[duck]

Hi mahima.. :)

you have correctly pointed out that "x" can take only even values. But, you did mistake while finding out probabilities.

Just try to figure out the no. of ways in which you can choose the cards and then arrange the cards.
Eg: x=2 it means you need to pick 1 green card and 1 red card.
Now, No. of ways of Choosing 1 green and 1 red is 5C1*5C1
and you can arrange the cards in 5!*5!
therefore, probability that x=2 is 5C1*5C1* 5!*5! /10!

Try to do for other values of "x".



:)

[Mahima]

oh yes!! i did take into consideration that when x is even, it half need to be green and half red.
sorry!

and thank you for correcting!! :) :)