## DEEBA Group Title 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 one year ago one year ago

1. Chelsea04 Group Title

1/8*1/9 so 1/72

2. Chelsea04 Group Title

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

3. Chelsea04 Group Title

it's wrong isn't it

4. agent0smith Group Title

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.

5. Chelsea04 Group Title

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

6. Chelsea04 Group Title

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

7. agent0smith Group Title

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

8. Chelsea04 Group Title

do you multiply that by 2?

9. Chelsea04 Group Title

yea, me too! been like 3 months

10. agent0smith Group Title

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

11. Chelsea04 Group Title

use a tree diagram, i'll draw one

12. agent0smith Group Title

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

13. agent0smith Group Title

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

14. agent0smith Group Title

$\left(\frac{ 8 }{ 17 } \times \frac{ 9 }{ 16 }\right) + \left(\frac{ 9 }{ 17 } \times \frac{ 8 }{ 16 }\right)$ I think this covers all possibilities...

15. Chelsea04 Group Title

yea, it does

16. Chelsea04 Group Title

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

17. agent0smith Group Title

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

18. Chelsea04 Group Title

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

19. DEEBA Group Title

is it the rite ans

20. Chelsea04 Group Title

$\left(\frac{ 8 }{ 17 } \times \frac{ 9 }{ 16 }\right) + \left(\frac{ 9 }{ 17 } \times \frac{ 8 }{ 16 }\right) = 2 \times \left(\frac{ 9 \times 8 }{ 17 \times 16 } \right) = 0.529$ 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%.