Question

Answer the following in one word, one sentence or as per the exact requirement:
I.If $P(E) = 0.2$ . Find $p($ not $E)$ .
II.What is the probability of a sure event?
III.If a coin is tossed $40$ times and $19$ times head comes and $21$ times tail comes. Write the probability of getting a head in a trial out of these 40 trial of the experiment.

Answer 1

Hint : Here, we need to solve the probability problem for the exact requirement to find the complement event of $E$ and the probability of a sure event and also do coin tossing of head and tail problem with respect to the given values.

Complete step by step solution:
I.Given, $P(E) = 0.2$
To find the value of $p($ not $E)$
By substitute the value in the complement event formula,

$$P(\overline E ) = 1 - P(E) \\\ P(\overline E ) = 1 - 0.2 = 0.8 \;$$

The final answer, $p($ not $E)$ is $0.8$ .

II.The probability of a sure event, $P(S) = \dfrac{{n(S)}}{{n(S)}} = 1$ , where $S$ is sample space.

III. Given,
A coin is tossed $40$ times
Head comes $19$ times
Tail comes $21$ times
To find the probability of getting a head in a trial out of these 40 trial of the experiment
$= \dfrac{{19}}{{40}}$

Note : In the coin tossing problem, tossing coins is an event and performing an experiment once is called trial. In a random experiment, each possible outcome is called an event. It will be a subset of the sample space.