Question

A coin is tossed $250$ times and the following results are obtained heads- $138$ , tails - $112$ . Find the probability of getting (a) heads (b) tail.

Answer 1

Hint : Probability is the state of being probable and the extent to which something is likely to happen in the particular situations or the favourable outcomes. Probability of any given event is equal to the ratio of the favourable outcomes with the total number of the outcomes.
$P(A) =$ Total number of the favourable outcomes / Total number of the outcomes

** Complete step-by-step answer** :
Here, a coin is tossed $250$ times.
Therefore, total number of the possible outcomes is $n(S) = 250$
The probability of getting Head
I.Let A be the event of getting head.
Given that head is obtained $138$
Therefore, the total number of favourable outcomes is $n(A) = 138$
Therefore, the probability
$P(A) = \dfrac{{n(A)}}{{n(S)}}$
Place values in the above equation –
$P(A) = \dfrac{{138}}{{250}}$
Take common factors from both the numerator and the denominator and remove them.
$P(A) = \dfrac{{69}}{{125}}$
So, the correct answer is “ $\dfrac{{69}}{{125}}$ ”.

II.The probability of getting Tail
Let B be the event of getting a Tail.
Given that head is obtained $112$
Therefore, the total number of favourable outcomes is $n(B) = 112$
Therefore, the probability
$P(B) = \dfrac{{n(B)}}{{n(S)}}$
Place values in the above equation –
$P(B) = \dfrac{{112}}{{250}}$
Take common factors from both the numerator and the denominator and remove them.
$P(B) = \dfrac{{56}}{{125}}$
So, the correct answer is “ $\dfrac{{56}}{{125}}$ ”.

Note : The probability of any event always ranges between zero and one. It can never be the negative number or the number greater than one. The probability of impossible events is always equal to zero whereas, the probability of the sure event is always equal to one.