Question

A coin is tossed 40 times and heads are obtained 23 times. If the coin is tossed at random, what is the probability of getting a tail?

Answer 1

First we have to define what the terms we need to solve in the problem are.
If a coin is tossed, we have two outcomes which are head and tail (coin has only two sides). And they have already given that head is obtained twenty-three times while the coin is tossed out of forty times;
Thus, again if the coin randomly we need to find the probability of getting the tails this time.
Formula used: $\text{Probability} = \dfrac{\text{Favourable event}}{\text{Total event}}$.

Complete step-by-step solution:
To find the required probability we need to use the formula of the favorable event probability;
$\text{Probability} = \dfrac{\text{Favourable event}}{\text{Total event}}$ the number of possible events divides the total given event.
Using this formula, we can say for $23$ heads we get $\text{Probability} = \dfrac{{23}}{{40}}{\text{ }}$ of getting the heads out of forty. Hence similarly we can find using the formula and method for the tail too.
Let in total forty times the coin is tossed and $23$ where heads; thus, for tails we have $40 - 23$ (overall coin tossed subtracts the heads out of this) solving this we get $40 - 23 = 17$ which is the possibility of getting the tails from the forty-coin tossed at random,
Hence applying this into the probability formula we get $\text{Probability} = \dfrac{{40 - 23}}{{40}}$ (overall minus the heads divides the total count) further solving we get the probability for the tails $\text{Probability} = \dfrac{{40 - 23}}{{40}} = \dfrac{{17}}{{40}}$ (number of favorable events is seventeen and the total event is forty)
Thus, the probability of getting tails from the coin is tossed at random is $\dfrac{{17}}{{40}}$

Note: If they ask us to find the percentage of getting tails; we need to use the percentage formula which is $\dfrac{{17}}{{40}} \times 100$ and further solving we get, $\dfrac{{17}}{{40}} \times 100= 42.5$ (is the percentage of getting tails from the coin tossed randomly) also we can able to from this $100 - 42.5 = 57.5$ is the percentage of getting heads from the coin toss.