Question

A box has 8 hard centred and 9 soft centred chocolates. two are selected at random.what is the probability that one is hard centred and other is soft centred

Answer 1

1/8*1/9
so 1/72

Answer 2

you find the probability of getting a hard centred: 1/8
then the probability of getting a soft centred: 1/9
then multiply them together

Answer 3

it's wrong isn't it

Answer 4

I think you may have to double your answer @Chelsea04 as you could get one hard, then one soft, or one soft, then one hard.

Answer 5

i'm thinking of a different question.
oh, right, yea. that i think makes much more sense

Answer 6

no! no! I got it now!
hard centred: 8/17
soft centred: 9/17
multiply these together
72/289

Answer 7

Yeah that sounds a bit better... been a while since i've done one of these.

Answer 8

do you multiply that by 2?

Answer 9

yea, me too! been like 3 months

Answer 10

Hmm i'm not sure if that's correct. It may be easier to do it using combinations...

Answer 11

use a tree diagram, i'll draw one

Answer 12

There's four possible outcomes: (h, h), (s,s), (h,s), (s,h)

Answer 13

(note not all are equally likely as there's 8 hard and 9 soft)

Answer 14

\[\left(\frac{ 8 }{ 17 } \times \frac{ 9 }{ 16 }\right) + \left(\frac{ 9 }{ 17 } \times \frac{ 8 }{ 16 }\right) \]

I think this covers all possibilities...

Answer 15

yea, it does

Answer 16

so basically in the end, you did need to multiply it by 2 ;)

Answer 17

Yep, but your original equation had them both over 17, not one over 17 and one over 16.

Answer 18

right, no replacement! Sorry, it's been a while

Answer 19

is it the rite ans

Answer 20

agent's is the right answer, follow his equation

Answer 21

\[\left(\frac{ 8 }{ 17 } \times \frac{ 9 }{ 16 }\right) + \left(\frac{ 9 }{ 17 } \times \frac{ 8 }{ 16 }\right) = 2 \times \left(\frac{ 9 \times 8 }{ 17 \times 16 } \right) = 0.529\]

So the probability is about 50%, which makes sense given our possible outcomes when picking two chocolates (h for hard, s for soft):

(h, h), (s,s), (h,s), (s,h)

If all options were equally likely, the probability would be exactly 50%.