A customer visiting the suit department of a certain store will purchase a suit with probability 0.22, a shirt with probability 0.30, and a tile with probability 0.28. The customer will purchase both a suit and a shirt with probability 0.11, both a suit and a tie with probability 0.14, and both a shirt and a tie with probability 0.10. A customer will purchase all 3 items with probability 0.06. What's the probability that a customer purchase: (a) none of these items? (b) exactly 1 of these items?

a. The probability that a customer purchase none of these items is 0.49

b. The probability that a customer purchase exactly 1 of these items would be of 0.28

Step-by-step explanation:

a. In order to calculate the probability that a customer purchase none of these items we would have to make the following:

let A represents suit

B represents shirt

C represents tie

P (A) = 0.22

P (B) = 0.30

P (C) = 0.28

P (A∩B) = 0.11

P (C∩B) = 0.10

P (A∩C) = 0.14

P (A∩B∩C) = 0.06

Therefore, the probability that a customer purchase none of these items we would have to calculate the following:

1 - P (A∪B∪C)

P (A∪B∪C) = P (A) + P (B) + P (C) - P (A ∩ B) - P (A ∩ C) - P (B ∩ C) + P (A ∩ B ∩ C)

= 0.22+0.28+0.30-0.11-0.10-0.14+0.06

= 0.51

Hence, 1 - P (A∪B∪C) = 1-0.51 = 0.49

The probability that a customer purchase none of these items is 0.49

b. To calculate the probability that a customer purchase exactly 1 of these items we would have to make the following calculation:

= P (A∪B∪C) - (P (A∩B) + P (C∩B) + P (A∩C) - 2 P (A ∩ B ∩ C))

=0.51 - 0.23 = 0.28

The probability that a customer purchase exactly 1 of these items would be of 0.28