A drawer holds 4 red hats and 4 blue hats. What is the

Question

A drawer holds 4 red hats and 4 blue hats. What is the probability of getting exactly three red hats or exactly three blue hats when taking out 4 hats randomly out of the drawer? 
(a) 1/8 
(b) Â¼ 
(c) Â½ 
(d) 3/8 
(e) 7/12

conocieur · Answer

I got

2 * ((4c3)*(4c1)) / (8c4)

= 16/35

none of the answers, i might be wrong

Professor · Answer

absolutly agree. thats what i got too. 

= 2   / (8c4) = 32/70 = 16/35

BG · Answer

If we use binominal formula (0,5+0,5)^4 the prob of getting 3R1B or 3B1R is 3C4*0,5*0,5^3=4/16=1/4

chillpill · Answer

can you explain this one? i was getting 16/35 myself too

remgeo · Answer

I am also getting 16/35

Total outcomes = C(8,4)

Favourable = C(4,3) * C (4,1) * 2

Probability = (C(4,3) * C(4,1) * 2 ) / C(8,4) = 16/35

swaroh · Answer

Made a mistake, i agree with 16/35.

Since it is "OR" should we not be adding.

Here is my take, i might be wrong.

Denominator= 8C4= 70

Numerator,

3 red hats out of 4 red hats and 1 Blue from 4 blue= 4C3*4C1=16
3 Blue hats out of 4 blue hats and 1 red from 4 red= 4C3*4C1=16

16/70 + 16/70= 16/35

Still i don;t see this in the answer choice.

Thanks

trivikram · Answer

BG can you please elaborate?

M8 · Answer

Professor would you please elaborate the numerator
2  ?
I see wht is 4C3, but what is '2' and 4C1 and why you multiply them?

Thank you.

conocieur · Answer

I thought about this approach too, even though it doesn't make too much sense, cause it would imply that every time you get one hat you put it back in the drawer and then pick a hat again, I would assume there is not replacement, but anyway even if we take BG's approach the answer would not be 1/4 but 1/2 as we have to consider 3reds - 1 blue or 1 red - 3 blues.

so taking the options from the question it would be 

1/2

old_dream_1976 · Answer

1/2 indeed 

Bionomial situation 

3 R = 4C3 x 1/16 

3R or 3R = 2(4C3 x 1/16) = 1/2

vipin7um · Answer

Unless I didn't understand the question properly, my answer is 2/5.

chillpill, pls post the OA and OE. And the source of the question as well.

Thanks,
Vipin

jlui4477 · Answer

What's the OA?

al1234 · Answer

Could it be 1/8 ?:)

Let p be the prob. to choose a red hat, and let q be the prob. to choose a blue one.

We should find P(exactly 3 blue or exactly 3 red)=qp^3+pq^3, where p = 4/8 and q = 4/8.

shevy · Answer

Getting 16/35 as well

A drawer holds 4 red hats and 4 blue hats. What is the

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