Homework Question

[rgrocks]

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

 

[arthur ohlsten]

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

 

[rgrocks]

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

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

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.

 

[arthur ohlsten]

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

 

[rgrocks]

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.

can u answer this question from my last post?