Question

Q.1. Probability is a measure of uncertainty. Are you agree with this? Justify your answer with examples.

Answer 1

SOLUTION

TO JUSTIFY

Probability is a measure of uncertainty

EVALUATION

In any random experiment if the total number of elementary ( simple) events in the sample space be n ( a finite number) among which the number of elementary events favourable to an event E , connected with the experiment be m then the probability of the event E is denoted by P (E) and defined as

$\displaystyle \sf{}P(E) = \frac{m}{n}$

Now the total number of possible outcomes = n and the total number of possible outcomes for the event E is m

So

$\sf{ 0 \leqslant m \leqslant n\: }$

$\implies \displaystyle \sf{ 0 \leqslant \frac{m}{n} \leqslant 1}$

$\implies \sf{0 \leqslant \: P(E) \: \leqslant 1}$

$\implies \sf{P(E) \in \: [ \: 0, 1 \: ]}$

For an impossible event, the number of favourable cases is zero and hence it's probability is 0

On the other hand for a certain event S all cases are favourable cases and hence it's probability is 1

0 and 1 are both certain number

From above we see that Probability is a measure of uncertainty. But it is also a measure of certainty.

EXAMPLE :

The probability of getting 53 Saturdays in a leap year :

Leap year = 366 days

366 days = 52 weeks 2 days

Now 52 weeks contains 52 Saturdays

2 days is one of the below

( Sunday, Monday), ( Monday, Tuesday), (Tuesday, Wednesday), ( Wednesday, Thursday), ( Thursday, Friday), ( Friday, Saturday ), (Saturday, Sunday)

So the total number of possible outcomes = 7

Let A be the event that of getting 53 Saturdays in a leap year

So the total event points for the event A is ( Friday, Saturday ), (Saturday, Sunday)

So the total number of possible outcomes for the event A is 2

Hence the required probability

= P(A)

$\displaystyle \sf{ = \frac{2}{7} }$

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