Question

.1) A company employs 40 skilled and 30 unskilled workers. Twenty five of the skilled workers and seventeen of the unskilled workers are college graduates. If an employee of the company is selected at random, the probability that the person picked will not be a college graduate is:

a) 2/5

b) 25/70

c) 12/28

d) 17/70

.2) If A is the event "tomorrow it will rain" and B is the event "I will win in the lottery", then:

           

a) A and B are mutually exclusive and independent events

                       

b) A and B are neither mutually exclusive nor independent

                       

c) A and B are mutually exclusive, but not independent

                       

d) A and B are independent, but not mutually exclusive

.3) How many five letters words can be made from 9 distinct letters if repetition is not allowed ?

a) 9⁵

b) 9C5

c) 9P5

d) 5⁹

.4) The expression P(A or B) = P(A) + P(B) is valid if:

a) A and B are independent

b) A and B are mutually exclusive   

c) A and B are dependent   

d) none of the above

Answer 1

1) Total number of employees = 40 + 3 = 70

total number of graduate employees = 25 + 17 = 42

Ungraduates = 70 - 42 = 28

probability of selecting a person will not be graduate = 28/70 = 2/5

option A

2) Both may be occur may be tomorrow, So Given two events are not mutually exclusive

And both the events are independent, since given two events are not effected one by another.

So

d) A and B are independent, but not mutually exclusive

3) The numebr five letters words can be made from 9 distinct letters = 9P5, since it is only arrangement.

So c) 9P5

4) if  A and B are mutually exclusive, then p(A and B) = 0

then only p(A or B) = P(A) + p(B)

So b) A and B are mutually exclusive