Question

FInd the probability P(E^c) if P(E)=0.28

Answer 1

Concepts and reason

The concept of probability is used to solve this problem.

The probability can be defined as a measure of likelihood that an event will occur. The probability will lie between 0 and 1 where 0 implies the impossibility of the occurrence of the event and 1 implies that the event will certainly occur where the outcomes of the random experiment consider as event.

The probability of an event does not occur can be calculated by subtracting the probability of occurrence of the event from 1.

Fundamentals

The probability, P for the complementary event can be calculated as:

$P\left( {{E^c}} \right) = 1 - P\left( E \right)$

Here, ${E^c}$ is the complimentary event of event $E$ .

For any event that is to occur its non-occurrence is the complimentary event. The sum of probability of any event and its compliment is one. So,

$\begin{array}{c}\\P\left( E \right) + P\left( {{E^c}} \right) = 1\\\\P\left( {{E^c}} \right) = 1 - P\left( E \right)\\\end{array}$

The probability for $P\left( {{E^c}} \right)$ is calculated as:

$\begin{array}{c}\\P\left( {{E^c}} \right) = 1 - P\left( E \right)\\\\ = 1 - 0.28\\\\ = 0.72\\\end{array}$

Ans:

The probability of compliment of event E is $P\left( {{E^c}} \right) = 0.72$ .

Answer 2

P(Ec) if P(E)=0.31