Question

A company that manufactures video cameras produces a basic model and a deluxe model. Over the past year, 41% of the cameras sold have been of the basic model. Of those buying the basic model, 31% purchase an extended warranty, whereas 48% of all deluxe purchasers do so. If you learn that a randomly selected purchaser has an extended warranty, how likely is it that he or she has a basic model

Answer 1

Answer:

$75.6\%$

Step-by-step explanation:

Let B be the event of buying a basic model.

Given that P(B) = 41%

Let D be the event of buying a basic model.

Given that P(D) = 1 - 41% = 59%

Let E be the event of extended warranty.

Given that:

P(E $\cap$ B) = 31% and

P(E $\cap$ D) = 48%

P(E) = P(E $\cap$ B) $\times$ P(B) + P(E $\cap$ D) $\times$ P(D)

P(E) = 31% $\times$ 41% + 48% $\times$ 59% = 0.4103

To find: P(B/E)

Formula:

$P(B/E) = \dfrac{P(E \cap B)}{P(E)}$

$\Rightarrow \dfrac{0.31}{0.41}\\\Rightarrow 0.756\\\Rightarrow 75.6\%$

So, the correct answer is $75.6\%$.