Question

Probability
A box contains 5 red bulbs, 4 blue bulbs and 3 yellow bulbs. 3 bulbs are selected randomly from the box.
Find the probability that all three bulbs are of different colours, given that one of them is yellow

Answer 1

the probability of a yellow is 3\12 so most likely they wood be red

Answer 2

@gorv

Answer 3

@dan815

Answer 4

If there are 12 bulbs and you select 3. The probability would be 3/12.

Answer 5

No it's not that simple

Answer 6

Answer is 5/9

Answer 7

@satellite73

Answer 8

hi
we can do this

Answer 9

I suppose it's a conditional probability. Isn't it?

Answer 10

you started with 12 light bulbs, but you know one is yellow, so now it is like having 11 light bulbs and you have to pick 2
yes, it is conditional

Answer 11

so change the problem to
you have 5 red, 4 blue, 2 yellow
you select 2
what is the probability that one is red and one is blue

Answer 12

\[(5C1\times4C1)/11C2\]

Answer 13

yeah that should do it
easier to write
\[\frac{5\times 4}{55}\]

Answer 14

So is this the final answer?

Answer 15

unless i miss my guess it is \(\frac{4}{11}\)

Answer 16

49
junyang96 Medals 0
So here's my tutor's explanation. the Probability
P( all 3 bulbs are of different colours| one yellow)
=P(all 3 bulbs are of different colours bulbs AND one yellow)/P(one yellow)
and since all 3 bulbs are of different colours is the subset of one yellow
so
=P(all 3 bulbs are of different colours)/P(one yellow)
=[5C1*4C1*3C1/12C3]/[3C1*9C2/12C3]
=5/9

Answer 17

@ganeshie8

Answer 18

looks you have a solution ?

Answer 19

I just want to know if which answer is correct. 5/9 or 4/11.

Answer 20

satellite's explanation sounds reasonable too

Answer 21

your tutor is conditioning on : "exactly one bulb being yellow"

Answer 22

yes

Answer 23

but that was not mentioned in the problem statement right ?

Answer 24

how do u know the condition is "exactly one bulb is yellow" or "atleast one bulb is yellow" ?

Answer 25

you get different answers based on how you interpret the problem

Answer 26

do you see how the phrasing is a bit ambiguous ?

Answer 27

your tutor is correct if we assume "exactly one bulb is yellow"

satellite is correct if we assume "atleast one bulb is yellow"

Answer 28

Thanks for the explanation. I suppose the question is saying exactly one bulb.

Answer 29

np :) lets fix the question then and work it again real quick :


A box contains 5 red bulbs, 4 blue bulbs and 3 yellow bulbs. 3 bulbs are selected randomly from the box.
Find the probability that all three bulbs are of different colours, given that `exactly one of them is yellow `

Answer 30

A : Exactly one of them is yellow
B : All of them different

Answer 31

\[\rm P( B|A) = \dfrac{p(A \cap B)}{P(A)}\]

you're using this formula, right ?

Answer 32

yes

Answer 33

\[\rm P(A) = \dfrac{\binom{3}{1}\binom{9}{2}}{\binom{12}{3}}\]

You can choose one yellow ball from the available 3 yellow balls in \(\binom{3}{1}\) ways

The remaining two balls can be selected in \(\binom{9}{2}\) ways

Answer 34

\[\rm P(A\cap B) = \dfrac{\binom{5}{1}\binom{4}{1}\binom{3}{1}}{\binom{12}{3}}\]

You're just picking one ball from each of the available colors

Answer 35

take the ratio

Answer 36

thanks