blog wrote:

A certain junior class has 1,000 students and a certain senior class has 800 students. Among these students, there are 60 siblings pairs , each consisting of 1 junior and 1 senior. If i student is to be selected at random from each class, what is the probability that the 2 students selected at will be a sibling pair?

A. 3/40,000

B. 1/3,600

C. 9/2,000

D. 1/60

E. 1/15

There are 60 siblings in junior class and 60 their pair siblings in the senior class. We want to determine probability of choosing one sibling from junior class and its pair from senior.

What is the probability of choosing ANY sibling from junior class? \(\frac{60}{1000}\) (as there are 60 of them).

What is the probability of choosing PAIR OF CHOSEN SIBLING in senior class? As in senior class there is only one pair of chosen sibling it would be \(\frac{1}{800}\) (as there is only one sibling pair of chosen one).

So the probability of that the 2 students selected will be a sibling pair is: \(\frac{60}{1000}*\frac{1}{800}=\frac{3}{40000}\)

Answer: A.This problem can be solved in another way:

In how many ways we can choose 1 person from 1000: \(C^1_{1000}=1000\);

In how many ways we can choose 1 person from 800: \(C^1_{800}=800\);

So total # of ways of choosing 1 from 1000 and 1 from 800 is \(C^1_{1000}*C^1_{800}=1000*800\) --> this is total # of outcomes.

Let’s count favorable outcomes: 1 from 60 - \(C^1_{60}=60\);

The pair of the one chosen: \(C^1_1=1\)

So total # of favorable outcomes is \(C^1_{60}*C^1_1=60\)

\(Probability=\frac{# \ of \ favorable \ outcomes}{Total \ # \ of \ outcomes}=\frac{60}{1000*800}=\frac{3}{40000}\).

Answer: A.Let’s consider another example:A certain junior class has 1000 students and a certain senior class has 800 students. Among these students, there are 60 siblings of four children, each consisting of 2 junior and 2 senior (I’m not sure whether it’s clear, I mean there are 60 brother and sister groups, total 60*4=240, two of each group is in the junior class and two in the senior). If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?

The same way here:

What is the probability of choosing ANY sibling from junior class? 120/1000 (as there are 120 of them).

What is the probability of choosing PAIR OF CHOSEN SIBLING in senior class? As in senior class there is only two pair of chosen sibling it would be 2/800 (as there is only one sibling pair of chosen one).

So the probability of that the 2 students selected will be a sibling pair is: 120/1000*2/800=3/10000

Another way:

In how many ways we can choose 1 person from 1000=1C1000=1000

In how many ways we can choose 1 person from 800=1C800=800

So total # of ways of choosing 1 from 1000 and 1 from 800=1C1000*1C800=1000*800 --> this is our total # of outcomes.

Favorable outcomes:

1 from 120=120C1=120

The pair of the one chosen=1C2=2

So total favorable outcomes=120C1*1C2=240

Probability=Favorable outcomes/Total # of outcomes=240/(1000*800)=3/10000

There are 60 sibling pairs. Probability of Selecting One Junior

[ With the breakdown being: P(John and his sibling) + P (Mary and her sibling) + P(Tom and his sibling) + .....

= (1/1000 x 1/800) + (1/1000 x 1/800) + (1/1000 x 1/800) + ..... and so on, until you add the 60 different possibilities ]