I realise that this is probably a really easy question I just don'y understand probability :(

There are 10 students in a class.

6 of the students are boys and 4 of the students are girls.

Three students are picked at random from the class to form a team.

Work out the probability that the team consists of 1 girl and 2 boys.

Posted Sat 9th June, 2012 @ 13:53 by

homz
I just did this on a practice paper, here is how I did it:

So basically draw a probability tree starting with one branch for boy and one for girl. For girl the probability is 4/10 and for boy it is 6/10. Then coming off of each of these you have another one saying boy and girl, only this time it is /9. You do this one more time with /8 and then look for the ones that have one girl and 2 boys. You times the three probabilities along the branch. Then you add the results that you got, and you have the answer!

Hope that made sense, otherwise look up how to do probability trees.

Answered Sat 9th June, 2012 @ 14:14 by

Freya
You need to make a probability tree, remembering it is conditional/dependant probability, as in the total amount will change every time somebody is selected.

1st person picked - 6/10 boys and 4/10 girls

2nd person picked (option 1) - 5/9 boys and 4/9 girls

2nd person picked (option 2) - 6/9 boys and 3/9 girls

3rd person picked (option 1a) - 4/8 boys and 4/8 girls

3rd person picked (option 1b) - 5/8 boys and 3/8 girls

3rd person picked (option 2a) - 5/8 boys and 3/8 girls

3rd person picked(option 2b) - 6/8 boys and 2/8 girls

this sound really confusing but put this information into a probability tree and multiply the fractions relating to the query: 1 girl and 2 boys, don't forget this query could appear in any order (1 boy, 1 girl then another boy)

When i drew this tree I got the answers:

6/10 x 5/9 x 4/8 = 0.166666667

6/10 x 4/9 x 5/8 = 0.166666667

4/10 x 6/9 x 5/8 = 0.166666667

add these answers together because these are 'or' answers = 0.500000001

which = 1/2 <---- there's your answer. You could also do this in a ratio way but I think this way makes more sense even though it is probably longer.

Answered Sat 9th June, 2012 @ 14:16 by

Laura^.^Edited by

Laura^.^ on Sat 9th June, 2012 @ 14:24

Thanks guys I understand it A LOT better now!!! ^_^

Answered Sat 9th June, 2012 @ 14:35 by

homz
use a tree diagram. Remember it's conditional/dependant probability.

6/10*5/9*4/8+6/10*4/9*5/8+4/10*6/9*5/8=1/2=0.5

Answered Sat 9th June, 2012 @ 14:17 by

Hoosierette