Question

A coin is tossed 1000 times with the following frequencies: Head: 455 and Tail: 555. When a coin is tossed at random, what is the probability of getting a tail?

Answer 1

Hint: Here we will use the formula of probability. Probability of any given event is equal to the ratio of the favourable outcomes with the total number of all the outcomes. Probability is the state of being probable and the extent to which something is likely to happen in the particular favourable situations. Here, we will find the probability by using the formula, $ P(T) = \dfrac{{n(T)}}{{n(S)}} $

Complete step-by-step answer:
Coin is tossed $ 1000 $ times and $ 455 $ times head and $ 555 $ times tail.
We know that probability of any event is No. of favorable outcomes by total no. of outcomes
Here we have been given that - Total no. of outcomes $ = $ Total no. of times coin tossed = 1000
Now Head comes $ 455 $ times and Tail comes $ 555 $ times.
When a random coin will be tossed it will either come as head or tail.
So, probability of getting a tail i.e. $ P(T) = \dfrac{\text{No. of times tail occurred}}{\text{No. of times coin tossed}}$.
 $ \Rightarrow P(T) = \dfrac{{n(T)}}{{n(S)}} $
Place the given values in the above equation –
 $
\Rightarrow P(T) = \dfrac{{555}}{{1000}} \\
\Rightarrow P(T) = 0.555 \;
  $
So, the correct answer is “0.555”.

Note: For this type of probability problems, just follow the general formula for probability and basic simplification properties for the fractions. Always remember that the probability of any event lies between zero and one. $ 1 $ . It can never be negative or the number greater than one. The probability of an impossible event is always zero.