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Interest centers around the nature of an oven

purchased at a particular department store. It can be

either a gas or an electric oven. Consider the decisions

made by six distinct customers.

(a) Suppose that the probability is 0.40 that at most

two of these individuals purchase an electric oven.

What is the probability that at least three purchase

the electric oven?

(b) Suppose it is known that the probability that all

six purchase the electric oven is 0.007 while 0.104 is

the probability that all six purchase the gas oven.

What is the probability that at least one of each

type is purchased?

Respuesta :

Using the concept of complementary probabilities, it is found that:

  • a) 0.6 = 60% probability that at least three purchase the electric oven.
  • b) 0.889 = 88.9% probability that one of each type is purchased.

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  • Two probabilities are complementary if their sum must be 100% = 1.

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Item a:

  • At most 2 and at least 3 are complementary.
  • 0.4 probability of at most 2.

Thus:

[tex]p = 1 - 0.4 = 0.6[/tex]

0.6 = 60% probability that at least three purchase the electric oven.

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Item b:

  • 0.007 probability of all electric.
  • 0.104 probability of all gas.
  • All the same types, and at least one of each are complementary.

The probability of all the same type is:

[tex]p = 0.007 + 0.104 = 0.111[/tex]

Thus, the probability of at least one of each type is:

[tex]p = 1 - 0.111 = 0.889[/tex]

0.889 = 88.9% probability that one of each type is purchased.

A similar problem is given at https://brainly.com/question/24622191

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