Hazel is a fussy eater She orders two appetizers The probabi

Hazel is a fussy eater. She orders two appetizers. The probability that she will like the first
appetizer is .4. The probability that she will like the second appetizer is .3. The probability that
she will like both appetizers is .12.
a) What is the probability that she likes neither appetizer?
b) Given that Hazel likes only one of the appetizers, what is the probability that it is the first
appetizer?
c) Is whether or not Hazel likes the second appetizer independent of whether or not she likes
the first appetizer? Use probability to explain how you know.

Please do a step by step walkthrough

Solution

a) Since the probability that she like either of the two appetizers = 0.4 + 0.3 - 0.12

                                                                                         =0.58

Hence the probability that she likes neither appetizer =1 - 0.58 =0.42

b) Using the conditional probability that the appetizer she likes is the 1st one = 0.4/0.58

                                                                                                                 = 0.69

c) As (0.4)(0.3)=0.12

Hence the liking of Hazel are independent