Question

Of all failures of a certain type of computer hard drive, it is determined that in 15% of them only the sector containing the file allocation table is damaged (F), in 65% of them only nonessential sectors are damaged (S), and in 20% of the case , both the allocation sector and one or more essential sectors are damaged.A failed drive is selected at random and examined.

a)Represent this information in Venn Diagram

b)Given that the drive has damaged file allocation sector.

1) what is the probability that some nonessential sectors are damaged as well?

2)what is the probability that no nonessential sectors are damaged?

c)Given that the drive has damaged nonessential sector.

1)what is the probability that file allocation sector is damaged as well?

2)what is the probability that allocation sector is not damaged?

Answer 1

(a) The problem can be represented as a venn diagram given below:

A= Allocation Sector

B= Non-essential sector

A and B= Allocation and Non-essential sector both

We are given

P(A) = Probability of allocation sector being damaged = 0.15 + 0.20 = 0.35

P(B) = Probability of non-essential sector being damaged = 0.65 + 0.20 = 0.85

P(A B) = Probability of both allocation sector and non- essential sector being damaged = 0.20

(b) (i)

Let event A= the allocation sector is damaged

B= the non-essential sector is damaged

We have to find P( B/A) and we know,

P( B/A ) = = = 0.57

(b) (ii) P( / A) = 1- P( B/A) = 1 - 0.57 = 0.43

(c) (i)

Let event A= the allocation sector is damaged

B = the non-essential sector is damaged

P( A/ B) = = = 0.23

(c) (ii) P( /B)= 1- P( A/B) = 1 - 0.23 = 0.77