and yh i got HW and i flop...

Q1) In a study of 120 pet-owners it was found that 57 owned at least one dog and of these 16 also owned at least one cat. There are 35 people in the group who didn't own any cats or dogs.

As an incentive to take part of the study, one participant is chosen at random to win a year's supply of pet food.

Find the probability of the winner of this prize...

a) Owns a dog but does not own a cat. [2 marks]

b) Owns a cat. [4 marks.. why?? ]

c) Does not own a cat given that they do not own a dog. [4 marks]

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Q2) A box of chocolates contains 20 chocolates, all of which are either hard or soft centred. Some of the chocolates contain nuts. 13 chocolates have hard centres of which 6 contain nuts. There are 10 nutty chocolates in total.

a)Represent the data in a Venn diagram

b)A chocolate is selected at random. Find the probability of:

(i) It having a soft centre.

(ii) It having a hard centre, given that it contains a nut?

c)A person chooses a soft centred chocolate at random. What is the probability that this chocolate contains a nut?

(d) If 3 different chocolates are selected at random without replacement. Find the probability that exactly one is a hard centre

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*cry cry* *sob sob*