Discussion Problems of the Day (14-06-11)

[varsha]

Suppose that a school band consists of 10 students from the freshman class, 20 students from the sophomore class, 3o students from junior class and 40 students from senior class.If 15 students are selected at random from the band, what is the probability that at least one student will be selected from each of the four classes ?

[Shruti]

hi Varsha..
By addition theorem I got the answer as >85 i.e. 17/20... So whats the correct answer n explation?

[Shruti]

I meant .85

[barkha]

hi shruti,

I am not sure what you exactly mean by addition theorem but you can use the following:
Define
A=No one is selected from the freshman class
B=No one is selected from the Sophomore class
C=No one is selected from the Junior class
D=No one is selected from the Senior class

We are interested in finding probability of intersection of the complements of the above Pr(A' ∩ B' ∩ C' ∩ D') = 1 - Pr(A U B U C U D)
We will use inclusion-exclusion principle to determine the probability of A U B U C U D
Pr(A U B U C U D) = Pr(A) + Pr(B) + Pr(C) + Pr(D) -  Pr(A ∩ B) - Pr(A ∩ C) - Pr(A ∩ D) - Pr(B ∩ C) - Pr(B ∩ D) - Pr(C ∩ D) + Pr(A ∩ B ∩ C) + Pr(A ∩ B ∩ D) + Pr(A ∩ C ∩ D) + Pr(B ∩ C ∩ D) - Pr(A ∩ B ∩ C ∩ D)
Now all of the above on the RHS are easy to get.

[reetika05]

Hi,

What is the answer to the question? I have got 83.5.

[barkha]

calculate the following to get the answer

1- 1/100C15{[90C15+ 80C15+ 70C15+ 60C15] - [70C15 + 60C15+ 50C15+ 50C15+ 40C15+ 30C15] + [40C15+30C15+20C15] }

[reetika05]

Thanks...