What is the probability that the two selected candies are the same flavour

| August 30, 2017

Question
Suppose we have two bowls full of candies. Each bowl contains four different flavours of candy – grape (which are purple), lemon (which are yellow), cherry (which are red) and raspberry (which are also red).

(a) We will randomly select one candy from each bowl. The outcome of interest is the flavour of each of the two candies. Write out the complete sample space of outcomes.

(b) Suppose instead that we randomly select one candy from each bowl, and the outcome of interest is the colour of each of the two selected candies. Write out the complete sample space of outcomes.

*Give all probabilities to four decimal places.

Bowl #1 contains 2 grape candies, 7 lemon candies, 8 cherry candies and 3 raspberry candies.

Bowl #2 contains 6 grape candies, 5 lemon candies, 2 cherry candies and 7 raspberry candies.

(c) What is the probability that the two selected candies are the same flavour?

(d) What is the probability that the two selected candies are different colours?

(e) What is the probability that the first selected candy is lemon or that the second selected candy is cherry?

(f) Let X be the number of grape candies that are selected. Find the probability distribution of X :

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