Question

Three companies A, B and C supply 25%, 35% and 40% of the notebooks to a school. Past
experience shows that 5%, 4% and 2% of the notebooks produced by these companies are not
of good quality. If a notebook was found to be bad quality, what is the probability that the
notebook was supplied by A?

Answer 1

Answer:

Step-by-step explanation:

→ Company A supply = 25% of the notebooks .

→ Defective notebooks = 5% of 25% = (5 * 25)/100 = 1.25% .

similarly,

→ Company B supply = 35% of the notebooks .

→ Defective notebooks = 4% of 35% = (4 * 35)/100 = 1.4% .

and,

→ Company C supply = 40% of the notebooks .

→ Defective notebooks = 2% of 40% = (2 * 40)/100 = 0.8% .

then,

→ Total notebooks supplied by three companies = 25% + 35% + 40% = 100% .

and,

→ Total defective notebooks = 1.25% + 1.4% + 0.8% = 3.45% .

therefore,

→ Required probability = 3.45 / 100 = (345/10000) = (69/2000) (Ans.)

Answer 2

The probability that the defective notebook was supplied by Company A will be 25/69

Step-by-step explanation:

Given:

Three companies A, B, & C supply 25%, 35%, & 40% of their notebooks to a school respectively

5%, 4%, 2% of these supplied notebooks are defective

To find:

the probability of company A supplying a defective notebook

Solution:

We find the probabilities of companies A, B, & C supplying a notebook

Probability of A supplying a notebook= P(A)= 25/100

Probability of B supplying a notebook= P(B)= 35/100

Probability of C supplying a notebook= P(C)= 40/100

Now, let's find the probabilities of companies A, B, & C supplying defective books out of their supply

Probability of A supplying a defective notebook= P(D/A)= 5/100

Probability of B supplying a defective notebook= P(D/B)= 4/100

Probability of C supplying a defective notebook= P(D/C)= 2/100

Total probability of supplying defective notebooks P(D)=

P(A) X P(D/A)+P(B) X P(D/B)+P(C) X P(D/C)

= 25/100 X 5/100+35/100 X 4/100+40/100 X 2/100

= 125/10000+140/10000+80/10000

P(D)= 345/10000

The probability that the defective notebook was supplied by the company A can be found by-

P(A/D)= P(A) X P(D/A)

                    P(D)

P(A/D)= 25/100 X 5/100

                345/10000

P(A/D)= 125/10000

             345/10000

P(A/D)= 125/10000 X 10000/345

P(A/D)= 125/345

P(A/D)= 25/69...............(dividing by 5)

∴ P(A/D)= 25/69

Thus, the probability of A supplying the defective notebook will be 25/69

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