Question

There are 40 elephants. 6 are blue, 8 black, 10 red, 6 yellow and 10 green. The 40 elephants are raced.

Given that there are exactly 4 red in the first 10 place what is the probability that there are 4 blue also

Answer 1

Use conditional probability
P(A|B)=P(A intersect B)/P(B)

Answer 2

we know that there are 4 red elephants accounted for, that leaves \(40-4=36\) elephants in our sample space
now we want the probability that 4 out of the 6 in first place are blue

Answer 3

lost the connection

Answer 4

number of ways to pick 6 out of 36 is
\[\dbinom{36}{6}\]
you want 4 blue and 2 not blue and not red
there are 6 blue total, the number of ways to pick 4 out of 6 is
\[\dbinom{6}{4}=\frac{6\times 5}{2}=15\]

Answer 5

the number of ways to pick 2 out the remaining not blue and not red elephants is
\[\dbinom{24}{2}=\frac{24\times 23}{2}=12\times 23=276\]

Answer 6

check my arithmetic here because i sort of lost my train of though during the blackout
in any case i believe you need to compute
\[\frac{\dbinom{6}{4}\times \dbinom{24}{2}}{\dbinom{36}{6}}\]

Answer 7

notice that in a conditional probability question like this one, you use what you know to narrow down the options

Answer 8

i tried it using conditional prob..
P(4B|4R) = (6C4x10C4x24C2 / 40C10) / (10C4x30C6/40C10) which cancels to (6C4x24C2) / 36C6.. is it wrong

Answer 9

(6C4x25C2) / 30C6 i mean

Answer 10

Given that there are exactly 4 red in the first 10 place

we know that there are 4 red elephants accounted for, that leaves 40−4=36 elephants in our sample space

doesnt exactly 4 red means that red cant be used anymore so 40-10=30 ?

Answer 11

oh maybe i was wrong

Answer 12

im not sure..

Answer 13

when you say "it is wrong" do you know the answer?

Answer 14

nope sorry this wass on the test.. left it blank though

Answer 15

ok let me try again

Answer 16

probability that 4 are red AND 4 are blue is
\[\frac{\dbinom{10}{4}\dbinom{6}{4}\dbinom{24}{2}}{\dbinom{40}{10}}\]

Answer 17

probability that 4 are red is
\[\frac{\dbinom{10}{4}\dbinom{30}{6}}{\dbinom{40}{4}}\]

Answer 18

yes i was wrong
divide and get
\[\frac{\dbinom{6}{4}\dbinom{24}{2}}{\dbinom{30}{6}}\]

Answer 19

you are right, the ten red ones are out of the picture
that is what i get for trying to think instead of using the formula

Answer 20

so what you wrote above
(6C4x25C2) / 30C6 is right, except i think you meant 24 and not 25

Answer 21

yup.. next part..
3 of the yellow elephants and tied together whilst 4 of the blue are tied toegher, what is the probability that these 7 elephants are in top 10?

Answer 22

hi asdhsadas