Question 1019415: There are 50MPs,two from each of 25 Tinkhundlas.
(i)If two MPs are chosen at random,what is the probability that they are from the same Inkhundla?
(ii)If ten MPs are randomly chosen to form a committee,what is the probability that they are all from different Tinkhundlas?
Answer by mathmate(429)   (Show Source):
You can put this solution on YOUR website!
Question:
There are 50MPs,two from each of 25 Tinkhundlas.
(i)If two MPs are chosen at random,what is the probability that they are from the same Inkhundla?
(ii)If ten MPs are randomly chosen to form a committee,what is the probability that they are all from different Tinkhundlas?
Solution:
Given 50 MPs two from each of 25 Tinkhundlas.
(i) If two are chosen at random (out of the 50), the first one has no constraints, but there is only one choice for the second one out of the 49 remaining, so probability is 1/49.
(ii)If ten are chosen to form a committee, the probability that they are all from different Tinkhundlas can be calculated as follows:
No limitation for the first one, so 50/50
The second one is chosen from 48, since her colleague must be excluded, so 48/49.
The third one is chosen from 46, so 46/48.
...
The tenth one is chosen from 32, so 32/41.
So the probability that they are all from different Tinkhundlas is
P(10 different)=(50/50)*(48/49)*(46/48)*....(32/41)
=
=0.3258 (approximately)
|
|
|
