Question

which of the following can be the probability of an event a 2, b -1, c 0.3 d 1.12​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

which of the following can be the probability of an event

a. 2

b. - 1

c. 0.3

d. 1.12

CONCEPT TO BE IMPLEMENTED

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

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

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

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

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

EVALUATION

We see from above that for any event A

$\sf 0 \leqslant P(A) \leqslant 1$

CHECKING FOR OPTION : a

Since 2 > 1

So 2 can not be probability of an event

CHECKING FOR OPTION : b

Since - 1 < 0

So - 1 can not be probability of an event

CHECKING FOR OPTION : c

$\sf Since \: \: 0 \leqslant 0.3 \leqslant 1$

So 0.3 can be probability of an event

CHECKING FOR OPTION : d

Since 1.12 > 1

So 1.12 can not be probability of an event

FINAL ANSWER

Hence the correct option is c. 0.3

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