Question

Gowri asked 25 people if they liked the taste of a new health drink. The responses are,

Responses	Like	Dislike	Undecided
No. of people	15	8	2

Find the probability that a person selected at random likes the taste.

Answer 1

Hint: We will categorize the responses as events. Then we will look at the formula to find the probability of an event occurring. The formula for the probability of an event is given as
$\text{probability of an event = }\dfrac{\text{number of outcomes in the event}}{\text{total number of outcomes}}$
We will use the formula to find the required probability.

Complete step by step answer:
The number of people Gowri asked their opinion about the taste of the new health drink is 25. So, the total number of outcomes is the total number of responses she received, which is 25. Let us categorize the responses as events as follows,
(i) Let A be the event in which people liked the taste of the drink. Therefore, the number of responses that fall into this event is 15.
(ii) Let B be the event in which people disliked the taste of the drink. So, the number of people that disliked the taste is 8.
(iii) Let C be the event in which people remained undecided about their opinion. There were 2 responses of this manner.
Now, we are asked to find the probability that a person picked at random will like the taste of the drink. This means that we have to find the probability of event A occurring.
The formula for finding the probability of an event is as follows,
$\text{probability of an event = }\dfrac{\text{number of outcomes in the event}}{\text{total number of outcomes}}$
We will substitute the values in the above formula,
$\text{P}\left( \text{A} \right)\text{ = }\dfrac{15}{\text{25}}$
Simplifying the above expression, we get the probability to be $\dfrac{3}{5}$ or $0.6$.

Note:
 It is useful to write all the events explicitly so that calculating the probabilities for these events becomes easier. Here, the number of people whose responses are recorded is known as the size of the sample space. We need to be careful while substituting the values in the formula, to avoid making minor mistakes.