Question

an experiment was conducted. Probabilities of an event was calculated by some students. which of the following could be the correct answer
A. 1.6
b. -2/5
c. 3/2
d. 2/3
plz explain it step wise plz​

Answer 1

The correct answer is option (D) i.e. 2/3.

• As we know that the probability of an event should always lie between 0 and 1 and can never be negative.
• In option (a) i.e. 1.6, the value is greater than 1 and hence can never be the probability of any event. Same is the case with option (C) i.e. 3/2.
• In option (B) i.e. -2/5 is a negative value which is not possible and hence the correct option must be option (D).

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

experiment was conducted. Probabilities of an event was calculated by some students. which of the following could be the correct answer

a. 1.6

$\displaystyle \sf{b. \: \: - \frac{2}{5} }$

$\displaystyle \sf{c. \: \: \frac{3}{2} }$

$\displaystyle \sf{d. \: \: \frac{2}{3} }$

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

CHECKING FOR OPTION (a)

Since

$\because \sf{ \: 1.6 > 1}$

So it can not be the probability of an event

CHECKING FOR OPTION (b)

$\displaystyle \sf{ \because \: \: \: - \frac{2}{5} < 0}$

So it can not be the probability of an event

CHECKING FOR OPTION (c)

$\displaystyle \sf{ \because \: \: \frac{3}{2} > 1 }$

So it can not be the probability of an event

CHECKING FOR OPTION (d)

$\displaystyle \sf{ \because \: \: 0 < \frac{2}{3} < 1 }$

So it can be the probability of an event

Hence the correct option is

$\displaystyle \sf{d. \: \: \frac{2}{3} }$

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Additional Information

• 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

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