Use the following scenario for all questions. The marketing manager of a grocery store observed customers going to the baby’s section. She found that 62% of all customers buy buby formula, 52% of all the customers buy diapers and 38% of all customers buy both baby formula and diapers. Use B to denote the event that a randomly selected customer buys baby formula and D to denote the event that a randomly selected customer buys diaper. Thus the information given above can be written as P(B)=0.62, P(D)=0.52 and P(B∩D)=0.38. _____________________________________________________________________________ What is the probability that a randomly selected customer buys either baby formula or diaper?

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joaobezerra joaobezerra · Answer 1 · 2020-02-26T15:43:34+01:00

Answer:

76% probability that a randomly selected customer buys either baby formula or diaper

Step-by-step explanation

We solve this problem building the Venn's diagram of these probabilities.

There are two events, events B and D.

We have that:

[tex]P(B) = P(b) + P(B \cap D)[/tex]

In which P(b) is the probability of only b and [tex]P(B \cap D)[/tex] is the probability of both B and D.

By the same logic, we have that:

[tex]P(D) = P(d) + P(B \cap D)[/tex]

P(B)=0.62, P(D)=0.52 and P(B∩D)=0.38.

So

[tex]P(D) = P(d) + P(B \cap D)[/tex]

[tex]0.52 = P(d) + 0.38[/tex]

[tex]P(d) = 0.14[/tex]

And

[tex]P(B) = P(b) + P(B \cap D)[/tex]

[tex]0.62 = P(b) + 0.38[/tex]

[tex]P(b) = 0.24[/tex]

What is the probability that a randomly selected customer buys either baby formula or diaper?

[tex]P(B \cup D) = P(b) + P(d) + P(B \cap D) = 0.24 + 0.14 + 0.38 = 0.76[/tex]

76% probability that a randomly selected customer buys either baby formula or diaper