a. What do you mean by objective and subjective probabilities? Fit one simple real-life example in each case, which really reflect its linkage to objective and subjective probabilities.

 

Q#:
a. What do you mean by objective and subjective probabilities? Fit one simple real-life example in each case, which really reflect its linkage to objective and subjective probabilities.

 

Objective probabilities

                                 Objective probabilities are based on mathematical analysis, experiments, and mathematical equations than anecdotes, personal experience, or hunting. In the financial world, taking advantage of opportunities can be very important to prevent from making emotional decisions when investing.

We often deceive ourselves into thinking that "we have always been lucky in car investments" or that "we have not lost money on gold"

Subjective Probabilities

                              The probabilities where we use our ideas, emotions and thoughts on the basis of past experience to find opportunities and probabilities. Example: we think,we have an 80% chance that our best friend will call today, because her car broke down yesterday and he will need a ride.

Example

let's say Ali buys a raffle ticket to support the local Girl Scouts home team. The team sells 1,000 tickets. From a standpoint, Ali has 1 in 1,000 chance of winning. But humbly, John thinks his chances of winning are very high because he "feels good about it." However, his chances are still 1 in 1,000.

            b. In a survey of 200 college students, it was found that;

 

            120 study mathematics,                     90 study physics

            70 study chemistry,                           40 study mathematics and physics,

            30 study physics and chemistry,       50 study chemistry and mathematics

            20 study none of these subjects.

Depict the events “A: Mathematics”, “B: Physics” and “C: Chemistry” on the given Venn-Diagram, and find the number of the students who studies all the three subjects. 

Solution#

Let Assume

A = Mathematics ; B = Physics and C = Chemistry 

n(A) = 120  ,  n(B) = 90  ,   n(C) = 70

n ( A ∩ B) = 40    ,       n ( B ∩ C ) = 30                                                               

n ( C ∩ A ) = 50    ,     n ( A∪B∪ C )’ = 20 

Now n(A∪B∪ C)’ = n(U) – n(A∪B∪ C) 

20 = 200 – n (A∪B∪ C) 

Therefore, n(A∪B∪ C) = 200 – 20 = 180 
n(A∪B∪ C) 
= n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(C ∩ A) + n(A ∩ B ∩ C)

180 = 120 + 90 + 70 - 40 - 30 - 50 + n(A ∩ B ∩ C)

⇒ n(A ∩ B ∩ C) =180 - 120 - 90 - 70 + 40 + 30 + 50 

⇒ n(A ∩ B ∩ C)

   = 20. (Students who studies all three subjects)