# Brand Probability is determined.

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A major hat store chain is having a sale on three nationally known 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. All three brands are manufactured by three independent companies.

Calculate the probability that:

a. None of the brands 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.

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##### Solution Summary

A major hat store chain's probabilities are configured.

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All 3 brands will be on sale

<br>For each of the brands, either they will sell or they won't sell.

<br>This is like tossing 3 On Sale coins

<br>But for a normal coin there is 1 chance in 2 of a head and 1 chance in 2 of a tail and the chances of No Sale or a Sale are 0.5:0.5 (50:50)

<br>Here

<br>For Brand A the chances of No Sale or a Sale are 0.3:0.7 (30:70)

<br>For Brand B the chances of No Sale or a Sale are 0.4:0.6 (40:60)

<br>For Brand C the chances of No Sale or a Sale are 0.5:0.5 (40:60)

<br>

<br>a) The probability that none will sell is the probability 3 No ...

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