Question

The Ambell Company uses batteries from two different manufacturers. Historically, 60% of the batteries are from manufacturer 1, and 90% of these batteries last for over 40 hours. Only 75% of the batteries from manufacturer 2 last for over 40 hours. A battery in a critical tool fails at 32 hours. What is the probability it was from manufacturer 2?

Answer 1

Answer:

The probability that the battery in a critical tool fails at 32 hours was from manufacturer 2 is 0.625

Step-by-step explanation:

Given that:

60% of the batteries are from manufacturer 1

90% of these batteries last for over 40 hours

Let the number of the battery duration be n = 0.90

Therefore n' = 1 - 0.90 = 0.10

Let p = manufacturer 1  and q = manufacturer 2

q = 1 - p

q = 1 = 0.6

q = 0.4

Thus ; 40% of the batteries are from manufacturer 2

However;

Only 75% of the batteries from manufacturer 2 last for over 40 hours.

Let number of battery duration be m = 0.75

Therefore ; m' = 1 - 0.75 = 0.25

A battery in a critical tool fails at 32 hours.

Thus; the that the battery in a critical tool fails at 32 hours was from manufacturer 2 is:

$= \dfrac{q \times m' }{ p \times n' + q \times m' }$

$= \dfrac{0.4 \times0.25 }{ (0.6 \times 0.1) + (0.4 \times 0.25 ) }$

$=\dfrac{0.1}{0.06+ 0.1}$

$=\dfrac{0.1}{0.16}$

= 0.625

The probability that the battery in a critical tool fails at 32 hours was from manufacturer 2 is 0.625