Question

Probability Question:

Ten boys and 12 girls decide to rent a 16-passenger van and a six-passenger car to drive to a rock concert in a nearby city. If the group is distributed randomly between the vehicles, what is the probability that
a) there are no boys in the car?
b) there are no girls in the car?
c) Alan and Margaret are both in the van?
d) there are more girls than boys in the car?

I just need help with C and D please...

Answer 1

So,have you heard about using C?

Answer 2

yes.

Answer 3

ah, I am lost, let's invite smarter people @amistre64

Answer 4

@hartnn

Answer 5

C is not discernable without an assumption

Answer 6

how did you determine a and b? the process is similar for c and d

Answer 7

Here's what I did for letter C:

Since Margaret and Alan is already in the van, then there will only be 20 people left.
And the available sits in the van will be 20.
So event A= 20C14 (20 sits for 14 people).

Then \(P(A)=\frac{20 C 14}{22C16}\) then I got the right answer. but i'm not sure if my reasoning makes sense..


For letter A: 12C6/22C6
For letter B: 10C6/22C6

Answer 8

gggbbb is equal

so

ggggbb or
gggggb or
gggggg

the sum of the individual probabilities gives us P([4,2] or [5,1] or [6,0])

Answer 9

you're doing letter D?

Answer 10

that was the concept for D yes

Answer 11

oh okay (: i'm also doing it.

what will be the sample space for this one?

Answer 12

the sample space for C im still trying to think of :) Zarkon or Satellite prolly can do it in thier sleep

Answer 13

since they 2 are already in the van
2 seats are filled
only 4 remains

Answer 14

12P4 * 10P2 out of 22P6 = 4g 2b in the car right?

P or C work the same in this case

Answer 15

i am bit confused though
6 passenger or 16 passenger ??

you used 16 for C but 6 for A,B ?

Answer 16

16 passenger seats for the van and 6 for the car

Answer 17

ok, so for C only, we consider 16

Answer 18

P and C are different though, aren't they? O.o
@amistre64

Answer 19

out of 22 sits (from car & van), 16 sits are from the van
so 22C16 is what i used for my sample space in letter C

Answer 20

they are are related: k! nCk = nPk

but i think i recall if all the terms are of the same 'kind' that we are fine

Answer 21

why 22 again ?
those 2 have fixed their seats
so 16 choices out of 20 remaining

Answer 22

ok, ignore me
you're finding sample space

Answer 23

so 20C14 / 22 C16 is correct
what was the doubt ?

Answer 24

so it's right? nothing, i just wanted to confirm (:

how about sample space in D?

Answer 25

i think C instead of P is better for my thought on d, tried some stuff with the wolf and failed at it lol

Answer 26

amistre's logic is correct for D
and yes, it should be nCr only

Answer 27

the right answer for D is 0.42 but I got 0.042

here's what I did:
I use Direct method: (12C6 x 10C0)+(12C5 x 10C1) + (12 C 4 x 10 C 2) =3119
Sample Space: 22C6 (because they are talking about the car)
so 3119/22C6=0.042

Answer 28

http://www.wolframalpha.com/input/?i=%2812+choose+4%29*%2810+choose+2%29%2F%2822+choose+6%29%2B%2812+choose+5%29*%2810+choose+1%29%2F%2822+choose+6%29%2B%2812+choose+6%29*%2810+choose+0%29%2F%2822+choose+6%29

Answer 29

31119/(22C6)

Answer 30

oh right! i'm missing one "1".

Thanks ! @amistre64 & @hartnn

Answer 31

good luck ;)

Answer 32

thanks for asking good questions :)