SOLUTION: please help. A box contains 20 chocolates, of which fifteen have soft centres and five hard centres. Two chocolates are taken at random, one after the other. Calculate the probabi

Question 519264: please help.
A box contains 20 chocolates, of which fifteen have soft centres and five hard centres. Two chocolates are taken at random, one after the other. Calculate the probability that

i. both chocolates have soft centres
ii. One of each sort of chocolate is taken
iii. Both types (soft and hard), given that the second chocolate has a hard centre.
Thank you.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A box contains 20 chocolates, of which fifteen have soft centres and five hard centres. Two chocolates are taken at random, one after the other. Calculate the probability that
i. both chocolates have soft centres
P(soft AND soft) = P(soft)*P(soft|soft) = (15/20)(14/19)=0.5526
ii. One of each sort of chocolate is taken
Since P(hard AND hard) = (5/20)(4/19) = 0.0526
P(one of each) = 1-[P(2 soft)+P(2 hard)] = 1-[0.5526+0.0526] = 0.3948
--------------------------------------------
iii. Both types (soft and hard), given that the second chocolate has a hard centre.
P(hard|soft) = P(hard and soft)/P(soft) = 0.3948/(15/20) = 0.5264
=====================
Cheers,
Stan H.

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