Probability of selecting a brother and sister at random

[silvertaurus]

There are 12 boys and 8 girls in a class, including a brother and a sister. If one boy and one girl are selected at random from the boys and girls respectively , what is the probability that the brother and sister are both selected?

 

[pka]

There are 12 boys and 8 girls in a class, including a brother and a sister. If one boy and one girl are selected at random from the boys and girls respectively , what is the probability that the brother and sister are both selected?

Did you read and agree with the before posting statement? You are required to show your workings.
What is the probability the brother is selected? What is the probability the sister is selected?
What do you think about both are selected?

 

[Dr.Peterson]

Please let us know what ideas you have tried, and where you are stuck; if you didn't already, read our submission guidelines.

Specifically, there are several very different ways to do this, and we'll want to give hints in line with what you have learned. Do you know about combinations and permutations? How about independent probabilities?

 

[Romsek]

Answer two questions and you're done.
a) how many ways can you select the brother and sister (should be obvious)
b) how many ways can you select 1 boy and 1 girl from the 12 and 8. (not obvious but shouldn't be hard)

divide a by b and that's your probability.

 

[Dr.Peterson]

Note that pka's hint uses the concept of independent probabilities, while Romsek's uses the concept of combinations. So you have a hint for whichever of the two general approaches you may have learned.

Let us know what you have done, and we can discuss more ideas if needed (or just congratulate you).