What do you mean by dependent and independent events? Fit one simple real-life example, which really reflect the concepts of dependent and independent events. There are five people applied for the position of chief executive of enterprises. Three of the applicants are over the age of 60 years. Two are female and one of them is over 60. i. What is the probability of a female person above 60?

Q#

What do you mean by dependent and independent events? Fit one simple real-life example, which really reflect the concepts of dependent and independent events.

 

Dependent events

Two events are dependentif the outcome of the first event affects the outcome of the second event, so that probabilities are changed.

Example

Let, we have 3 black and 6 green balls in a bag.  We pull out one ball, which may be black or green.  Now there are 8 balls left in the bag. Now if we draw another ball from the bag, now the color of ball drawn, will be effected by the color of balls drawn in first event, so these two events are dependent.

Independent events

Two events are called independent, if the probability of one event is independent of occurrence or non-occurrence of other events.

Example

if we put a coin in the air and get the result as Head, we will again if we put the coin but this time we get the result as Tail. In both cases, there is a difference between the two. Its means that in both of the events the outcomes are independents.

 

 

a.      There are five people applied for the position of chief executive of enterprises. Three of the applicants are over the age of 60 years. Two are female and one of them is over 60.

i.                    What is the probability of a female person above 60?                               

 

Let suppose

A be the event that applicant is male

            B denotes the event that applicant is female

                    C be an event that the applicant is over the 60 years old

P(A) = 3/5

P(B) = 2/5

P(C) = 3/5

P(C/B) = 1/2

   P(C/A) = 2/3

    P(B and C) = P(C/B) P(B)

                    =  0.5 * 0.4

                    = 0.2  = 20%   Answer

                    If a person is male, what then is the probability of a male below 60?       

                                 P(C/A) =

                               P( A and C) = P(C/A) P(A)

                                                   = 0.40

                                P(C/A) = 0.40/0.60

                                            = 0.666

                    P(Less than 60) = 1-0.666

                                             = 0.333

                                          =33.3%   Answer

 

ii.                  If a person is over 60, what then is the probability of a female above 60?          [Marks-03]

                       P(B/C) =

                                            = 0.2/0.6

                                 = 0.333

                                   = 33.3%    Answer