A male customer visiting the suit department of a certain store will purchase a suit with probability 0.16, a shirt with probability 0.18, and a tie with probability 0.2. The customer will purchase both a suit and a shirt with probability 0.07, both a shirt and a tie with probability 0.09, and with no probability of purchasing a suit and a tie.
(a) What is the probability that a customer purchases at least one of these items?
P = 0.16 + 0.18 + 0.2 - 0.09 - 0.07 = 0.38
(b) Given that the customer purchases a shirt, what is the probability that he also purchases a tie?
P = 0.09/0.18 = 0.5
(c) Given that the customer purchases at least one item, what is the probability that he purchases a shirt and a tie?
I am confused about this part on conditional probability, as the context is different from part b. Would be very grateful to receive any constructive feedback regarding my question. Thank you!