Question

1)Explain why probability is important in decision making.

2) Think of the following two possibilities:

A) You have never caught a fish

B) You have caught a fish longer than 12 inches

...Which of the following is true: 1) A & B are mutually exclusive and collectively exhaustive

2) A & B are mutually exclusive but not collectively exhaustive

3) A & B are not mutually exclusive but are collectively exhaustive

4) A & B are not mutually exclusive nor collectively exhaustive

3) If you use a fair coin with heads on one side and tails on the other, what is the probability of flipping 3 heads in a row?

Answer 1

Answer to Question 1:

Probability is important in case of making decisions under uncertainty. Under uncertainty, a decision can have multiple outcomes. But chances of each outcome happening are different and thus we can say that there will be multiple outcome with different probability of occurrence. Each outcome will have their respective expected value

To summarize , when one makes decision under uncertainty, there will be multiple outcome with their respective expected values and corresponding probabilities.

It will be prudent to choose the outcome which will have the highest value of “Probability x Expected outcome “ since that will give the true picture of the best outcome. Probability thus is an important determining factor for decision making under uncertain situation.

Answer to question 2 :

Undoubtedly , Never catching a fish and Catching a fish are two mutually exclusive events.

Two statements with one highlighting the act of catching a fish and another the act of never catching a fish can also be considered as two exhaustive items.

However never catching a fish and catching a fish longer than certain length are not two exhaustive events as there will be multiple possibilities of catching fishes with minimum length restrictions.

Therefore,

ANSWER : C ) A& B ARE MUTUALLY EXCLUSIVE BUT NOT COLLECTIVELY EXHAUSTIVE

Answer to question 3 :

Probability of flipping a head while tossing a coin = ½

Since, flipping a coin three times are three mutually independent events, probability of flipping 3 heads in a row

= Probability of flipping head in first flipping x Probability of flipping head in 2^nd tossing x Probability of head in third flipping

= ½ x ½ x ½

= 1/8

PROBABILITY OF FLIPPING 3 HEADS IN A ROW = 1/8