Exercise 3d Tree Diagrams, Section B, Question 2. (Page 201)

A box contains20chocolates, of which15have Soft centres and5have Hard centres. Two chocolates are taken at random,one after the other.

Calculate the probability that

(a)both chocolates have Soft centres,[BOOK ANSWER:]

(b)one of each sort of chocolates is taken,[BOOK ANSWER:]

(c)both chocolates have Hard centres,given thatthe second chocolates has a Hard centres.[BOOK ANSWER:]

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I manage as shown below, to successfully obtain the first two answers correct, but question(c)don't corresponds to any solutions that I could ever think of.

My Solution:

(a)

MATCHED

(b)

MATCHED

(c)I need Help here, this conditional probability is ok I hope:

MISMATCHED !!!

Is it a mistake of interpretation from my part or from the Book? Your Help is welcomed, Thank you