Homework Question

a) A group of 5 boys and 10 girls is lines up in a random order, what is the probability that the person in the 4th position is a boy?
b) what about the person in the 14th position
c) what is the probability that a particular boy is in the 3rd position?

First i figured out that 15! is the number of possibilities to organize the 15 children. From this point on I am not sure at all
B=Boys G=Girls

Probability that u will select a boy at all in any position, P(B)=5/15 = .333

so i figured that the probability of a person on the 4th position being a boy is 33% because thats the probability that u will have a boy in any position
and i figure thats the same for the 14th position

the probability that a particular boy is in the 3rd position confuses me because that means the probability that a certain anyone (A) would be P(A)=1/15 = 0.066 = 7%

can someone explain this problem to me using more mathematical vocabulary so i can make sense of these new terms.
I just learned what probability, permutation, and combination is.

Thanks

5 boys 10 girls
[C is my notation for Combinations aCb means from a you choose b]

probability of boy in any position:
from the 5 boys you choose 1, and from the 10 girls you choose 0, from the total of 15 you choose 1

[5 C 1 x 10 C 0] / 15 C 1
5!/[4!1!] x 10!/[10!0!] /[ 15!/1!14!]
5x1/15
1/3 answer
==========================================================================

a boy A and 4 more boys and 10 girls
you choose A and 1boy from the remaining 4 and 0 girls
1 x 4 C 0 x 10 C 0 / [15 C 1]
1x [4!/(0!4!)] x [10!/(0!10!)] / [15!/(14!1!)]
1x 1x1 /15
1/15 answer

Arthur

probability of boy in any position:
from the 5 boys you choose 1, and from the 10 girls you choose 0, from the total of 15 you choose 1

[5 C 1 x 10 C 0] / 15 C 1
5!/[4!1!] x 10!/[10!0!] /[ 15!/1!14!]
5x1/15
1/3 answer

Click to expand...

what general formula is that? i dont get how you knew to use that formula. 5 C 1 = the number of combination we can choose 1 boy from a group of 5. 10 C 0 is the number of combination we can choose 0 girls from 10. why did u chose to multiply the two values? why did we chose to divide the whole thing by 15 C 1 which is the number of combinations i can choose 1 from 15.? wouldnt it make more sense to divide it just by 15! the total number of permutations? please explain further.

i assume this was the solution to problem c)

a boy A and 4 more boys and 10 girls
you choose A and 1boy from the remaining 4 and 0 girls
1 x 4 C 0 x 10 C 0 / [15 C 1]
1x [4!/(0!4!)] x [10!/(0!10!)] / [15!/(14!1!)]
1x 1x1 /15
1/15 answer

Click to expand...

why am i selecting boy A and 1 more boy from the remaining 4? who is this extra boy aside from boy A. Boy A is the specific boy in the third position? so why do we need to know about this second boy? then the solution confuses me more

so the combo\ination that i get 0 boys from the 4 boys left (4 C 0) is multiplied by 1 (why?) is multiplied by the combination that we get 0 girls from the 10 (10 C 0) (why do we have to multiply these to combination's? what does it mean).

please explain i know im helpless and my statistics book isnt making it easier and my professor doesnt explain much because he is always rushing to cover material.

when you say AND you multiply and when you say OR you add

what is the probability of choosing 1 boy from the 5' AND' 0 girls from the 10
the and says multiply
Choose 1 from the total of 15
one boy from five is 5 C 1
zero girls from ten 10C 0

multiply these two because we said AND

divide by 15 C 1

hope this answers your question
Arthur

why am i selecting boy A and 1 more boy from the remaining 4? who is this extra boy aside from boy A. Boy A is the specific boy in the third position? so why do we need to know about this second boy? then the solution confuses me more

so the combo\ination that i get 0 boys from the 4 boys left (4 C 0) is multiplied by 1 (why?) is multiplied by the combination that we get 0 girls from the 10 (10 C 0) (why do we have to multiply these to combination's? what does it mean).

please explain i know im helpless and my statistics book isnt making it easier and my professor doesnt explain much because he is always rushing to cover material.

Click to expand...

can u answer this question from my last post?