Question

A coin is tossed 150 times and the outcomes are recorded. The frequency distribution of the outcomes H(i.e. head) and T(i.e. tail) is given below:

Outcome	H	T
Frequency	85	65

Find the value of P(H), i.e., probability of getting a head in a single trial.
A. $P\left( H \right) = 0.769$(approx.)
B. $P\left( H \right) = 0.663$(approx.)
C. $P\left( H \right) = 0.567$(approx.)
D. None of these

Answer 1

First note the number of favorable outcomes and the total number of outcomes, then use the general formula of finding the probability which is given as:
$P\left( H \right) = \dfrac{{{\text{Number of favorable events}}}}{{{\text{Total possible outcomes}}}}$

Complete step-by-step answer:
It is given in the problem that a coin is tossed 150 times and the frequency distribution of the outcomes H(i.e. head) and T(i.e. tail) is given below:

Outcome	H	T
Frequency	85	65

We have to find the value of P(H), i.e., the probability of getting a head in a single trial.
The frequency of getting heads is 85 and the coin is totally tossed for 150 times.Now, assume the number of favorable ways as the number of frequency of getting heads, and the total number of possible outcomes as the number of times the coin is tossed.
Then the probability is given as the ratio of the number of occurring favorable events to the number of total possible number of outcomes. That is,
$P\left( H \right) = \dfrac{{{\text{Number of favorable events}}}}{{{\text{Total possible outcomes}}}}$
Number of favorable outcomes=85 and Total possible outcomes=150
Substituting the values in the formula:
$P\left( H \right) = \dfrac{{85}}{{150}}$
Simplifying the fraction and express in the decimal form:
$P\left( H \right) = 0.5666666$
Rounding off the value to hundredth place:
$P\left( H \right) \approx 0.567$
So, the approximate probability of getting head in a single trail.

So, the correct answer is “Option C”.

Note: Favorable event defines a possibility of happening a particular event. In the given problem, the frequency of getting heads is the favorable event and total times, the coin is tossed is taken as the possible outcomes.