Question

In a city, 20 % of people watch star news, 40 % watch star plus, 10 % star sports, and remaining watch discovery. If there is electricity in only 1 house and a channel is being watched. What is the probability that star news is being watched?
(a). 0.5
(b). 0.4
(c). 0.2
(d). 0.1

Answer 1

Hint: Percentage is calculated using the formula \[{\text{Percentage}} = \dfrac{{{\text{Required Value}}}}{{{\text{Total Value}}}} \times 100\% \]. Probability is calculated by using the formula \[{\text{Probability}} = \dfrac{{{\text{N(E)}}}}{{{\text{N(S)}}}}\]. Then using this find the probability that star news is being watched.

Complete step-by-step answer:

The percentage of a quantity means a fraction of the quantity expressed by taking a hundred as a whole. 100 % means the entire quantity or the whole. The word percent comes from the Latin word Per Cent where Cent means a hundred.
When we have the total number, we just multiply it with the percentage and divide by 100 to get the required value.
Let us assume that there are 100 people in the city. It is given that 20 % of people watch star news, 40 % watch star plus, 10 % star sports and remaining watch discovery and only 1 house has electricity. We need to find the probability that star news is being watched.
Let the event E be that star news is being watched, then if N(E) is the number of favorable outcomes and N(S) is the total outcomes, then, we have:
\[{\text{Probability}} = \dfrac{{{\text{N(E)}}}}{{{\text{N(S)}}}}\]
The number of people watching star news can be found from the given percentage. Hence, we have:
\[{\text{N(E)}} = \dfrac{{20}}{{{\text{100}}}} \times 100\]
Simplifying, we get:
\[{\text{N(E)}} = 20\]
The total number of people in the city is 100. Hence, we have:
\[{\text{N(S)}} = 100\]
Hence, the probability is given as follows:
Probability = \[\dfrac{{{\text{20}}}}{{{\text{100}}}}\]
Probability = 0.2
Hence, the correct answer is option (c).

Note: You can also find the answer directly from the percentage. The percentage itself gives the probability when the fraction for a hundred is evaluated, hence, 20 % is 0.2.