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.