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Certain and Impossible Events

If an event c...

Question

If an event cannot occur i.e. it is an impossible event, then its probability is _________.

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Solution

If an event cannot occur i.e. it is an impossible event, then the number of outcomes in the favour of the event are 0. Thus, the probability of occurrence of an impossible event is always 0.

If an event cannot occur i.e. it is an impossible event, then its probability is 0.

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Similar questions

Q. Fill in the blanks:
(i) The probability of an impossible event is ........ .
(ii) The probability of a sure event ......... .
(iii) If E is an event and P(E) = p then p(not E) = ........ .
(iv) If E is a possible event and it is not a sure event then P(E) lies between ...... and ....... .
(v) P(E) + P(not E) = ........ .
(vi) The probability of occurrence of an event cannot be greater than ....... .

Q. If the probability of a sure event is A and an impossible event is B, then (A + B) equals

Q. Consider four independent trials in which an event

A

occurs with probability

\frac{1}{3}

B

will occur with probability

1

A

occurs at least twice, it can not occur if the event

A

does not occur and it occurs with a probability

\frac{1}{2}

A

occurs once. If the probability

p

of the occurrence of event

B

can be expressed as

\frac{m}{n},

m, n \in N,

then the least value of

m + n

Q. Fill in the blanks:

(i) Probability of a sure event is ...............

(ii) Probability of an impossible event is ................

(iii) The probability of an event (other than sure and impossible event) lies between .................

(iv) Every elementary event associated to a random experiment has .............. probability.

(v) Probability of an event A + Probability of event 'not A' = ................

(vi) Sum of the probabilities of each outcome in an experiment is ................

Q. If the probability of an event of a random experiment is

P (E) = 0

, then the event is called an impossible event is

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