A certain circuit board consists of two resistors, green and red. The circuit bo

Question

A certain circuit board consists of two resistors, green and red. The circuit board manufacturer has two huge bins filled with the resistors, one for each color. Based on several years of data, it is known that 90% of the red resistors are functional, and 75% of the green resistors are functional. When creating a circuit board, the technician selects one red and one green resistor at random

(a) The circuit board as a whole is only functional if both resistors are functional. What is the probability that the circuit board is functional?

(b) What is the probability that exactly one of the resistors chosen is functional?

Explanation / Answer

What is the probability that the circuit board is functional?

we have given that the probability of red resistors functioning = 0.9 and the probability of green resisters functions well = 0.75.

that is the probability that the red resistors not functioning well = 0.1. and the probability that the green resistors not functioning well = 0.25.

a] the probability that the circuit board is functional = 0.9*0.75 = 0.675

b] the probability that exactly one of the resistors chosen is functional = 0.9*0.25 + 0.75*0.1 = 0.3

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