Answer:
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
Multiply all terms by 15
3x+3x= 10x+30
Combine like terms
6x=10x+30
Subtract 10x from both sides
-4x=30
Divide both sides by -4
x= -7.5
Final answer: -7.5
