Question

A coin is tossed 1500 times with the following frequencies:
Head: 655 Tail: 845
Compute the probability for each event.

Answer 1

Hint : When a coin is tossed, then there are only two possibilities of events that are possible, which means the result of this event is either “Heads” or “Tails.” Now, if the coin is tossed a number of times, then the resulting events are repeated. These repeated events or the occurrences of the events more than once are known as the “Frequencies of the event”.

Complete step-by-step answer :
Let the number of times the coin is tossed be $n$ , the frequency of head be $H$ and the frequency of the tail be $T$, then
The number of times the coin is tossed $n = 1500$
So total possibilities of this event $n = 1500$
Also, the number of occurrence or the frequency of head $H = 655$
And the number of occurrence or the frequency of tail $T = 845$
So, the probability of coming heads $P\left( H \right) = \dfrac{H}{n}$
Substituting the values of $H$ and $n$ we get,
$\begin{array}{c} P\left( H \right) = \dfrac{{655}}{{1500}}\\\ = 0.436 \end{array}$
Similarly,
The probability of coming tails $P\left( T \right) = \dfrac{T}{n}$
Substituting the values of $T$ and $n$ we get,
$\begin{array}{c} P\left( T \right) = \dfrac{{845}}{{1500}}\\\ = 0.563 \end{array}$
Therefore, the probability of Heads is 0.436 and the probability of Tails is 0.563.

Note : The probability of any event, no matter how many times the event has occurred, is always less than or equal to 1. If the probability of the event is 1, then it means that the event is a “certain event,” and if the probability of the event is 0 then it means that the event is an “impossible event.”