Probability

[edwim12]

Question 1. A major shoe store is selling brands A,B and C. Probabilities that Brand A,Brand B, or Brand C will not be big sellers are: 0.30,0.40,and 0.50 respectively Brands are from 3 independent companies. Calculate the probability that:

a. none of the brand will be big sellers.
b) exactly two brands will be big sellers
c) exactly one brand will be a big seller
d) all three brands will be big sellers.

The formulas I used in the solutions are:
a) P(none of the brand will be big sellers) = P(not A and not B and not C)
b) P(exactly two brands will be big sellers) = P( A and B) + P( A and not C)
P(B and not C) + P(A and C)
c) P( exactly one brand will be a big seller) = 1- part b
d) P(all three brands will be big sellers)= P (A and B and C), however if I take the complement of part a, it is not the same answer.

Thanks in advance. Edwim12

[quark]

Hi edwim12,

b) P(exactly two brands)=P(A and B and not C)+P(A and not B and C)+P(not A and B and C)

c) P(exactly one brand)=1-partb-P(all three brands will be big sellers)
or P(exactly one brand)=P(A and not B and not C)+P(not A and B and not C)+P(not A and not B and C)

d) the complement of A is {at least one brand will be big selllers} the probability will be larger than P(all three brands will be big sellers).

[edwim12]

Thank you so much quark