We have learned the following about a group that likes to eat salmon: 60% of this group are
women, the rest are men. Among the women who like to eat salmon, 70% also like to eat it
sushi. Among the men who like to eat salmon, 50% also like to eat sushi. Use "M"
and "K" to refer to men and women respectively, and let "S" stand for the event that a
person likes sushi.
(a) i. Create a probability tree that shows the information given in the task text. Make it clear which probabilities are listed along all the different ones
the branches in the probability tree you submit: It should e.g. stand P(K) = 0.60
along one of the branches.
ii. Make a cross table showing the probabilities for the different sections K ∩ S,
M ∩ S, K ∩ S and M ∩ S.
(b) i. Find the probability that a random person from this group is one who
likes to eat sushi.
ii. Find the probability that a random person from this group is a man
who likes to eat sushi.
iii. Find the probability that a random person from this group is a man,
given that we know that person likes to eat sushi.
(c) Briefly explain why the events "M" and "S" are not independent events. Note:
If you have not achieved the previous assignments, you can do so in this sub-assignment
payoff by briefly explaining how we must proceed to show independence between
two events.