Problem Solving

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

Answer - 3/40,000

My Answer - Prob. of chosing 1 from senior - 60/1,000
prob. of chosing 1 from Junior - 1/800
OR
prob. of chosing 1 from junior - 60/800
prob. of chosing 1 from senior - 1/1000
Ans = (60/1,000 * 1/800) + (60/1,000 * 1/1000)
=2*3/40,000
=3/20,000

Could someone please tell me what is wrong in my reasoning?

Any help appreciated. Thanks.

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

Answer - 3/40,000

My Answer - Prob. of chosing 1 from senior - 60/1,000
prob. of chosing 1 from Junior - 1/800
OR
prob. of chosing 1 from junior - 60/800
prob. of chosing 1 from senior - 1/1000
Ans = (60/1,000 * 1/800) + (60/1,000 * 1/1000)
=2*3/40,000
=3/20,000

Could someone please tell me what is wrong in my reasoning?

Any help appreciated. Thanks.

The questions is only about selection. You are duplicating the case by involving permutation. For example if you have to select x and y, you select x first and than y or select y first and than x is all same. When you say selecting x first is different from selecting y it's arrangement than.

The question here is about selecting siblings so you select one sibling from junior and than from senior is same as selecting one from senior and than from junior. Don't duplicate the case by considering the order of selection(arrangement)

60/1000*1/800 =60/800000 =6/80000=3/40000

Thanks,
Quant-Master

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

Answer - 3/40,000

My Answer - Prob. of chosing 1 from senior - 60/1,000
prob. of chosing 1 from Junior - 1/800
OR
prob. of chosing 1 from junior - 60/800
prob. of chosing 1 from senior - 1/1000
Ans = (60/1,000 * 1/800) + (60/1,000 * 1/1000)
=2*3/40,000
=3/20,000

Could someone please tell me what is wrong in my reasoning?

Any help appreciated. Thanks.

You should not be adding the two...its one or the other...

there are two ways you could go...
Approach 1 ) first select from junior class and then select from senior class...
The probability of choosing a student from junior class who has a sibling = 60/1000.
The probablity of choosing a student from senior class who is a sibling of the student selected from junior class = 1/800

So probablity of two students selected being siblings = (60/1000) * (1/800) = 3/40,000

Approach 2) first select from senior class and then select from junior class...

The probability of choosing a student from senior class who has a sibling = 60/800.
The probablity of choosing a student from junior class who is a sibling of the student selected from senior class = 1/1000

So probablity of two students selected being siblings = (60/1000) * (1/800) = 3/40,000

Hope it helps.

Can't we c that way...
Prob of selecting 1 student from Junior Class = 1/1000.
Prob of selecting 1 student from senior class = 1/800.
So selecting 2 students from junior and senior class = 1/1000*1/800.
Now we have 60 pairs of siblings.
Selecting 1 pair is 60 ways.
So, prob of selecting 1 pair of siblings from this junior and senior class = 60*1/1000*1/800.