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Question

Match the following types of events to their probability.

A
1
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B
0<P(E)<1
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C
0
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Solution

We know that the probability of an event E occurring is given by:

P(E)
=Number of favourable outcomesTotal number of outcomes

Let the number total number of outcomes of a certain experiment E be n.

Let a be the number of favorable outcomes in experiment E.

In the case of certain events, all the outcomes that turn up are favorable.

Hence, n=a.

P(E)=nn=1

The probability of certain events is 1.

In the case of Impossible events, none of the outcomes that turn up are favorable outcomes.

Hence, a=0.

P(E)=0n=0

The probability of impossible events is 0.

In the case of Probable events, some but not all of the outcomes that turn up are favorable outcomes.

Hence, 0<a<n.

P(E)=an

The probability of probable events is 0<P(E)<1

Hence:

0<P(Probable Event)<1

P(Certain Event)=1

P(Improbable Event)=0


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