Question

A bag has 5 red balls and 7 yellow balls. (The balls are identical in all respects other than color). A ball is drawn from the bag without looking into the bag. What is the probability of getting a yellow bag?

Answer 1

Hint:For a random event, the probability of an event, say p(E) is defined as the ratio of the number of favorable outcomes or chances and the total number of outcomes. Here,$P(E) = \dfrac{{N(A)}}{{N(S)}}$, where $N(A)$ is number of favorable outcomes and $N(S)$ is the total number of outcomes.There are total 12 balls in the bag and number of yellow balls is 7.So, according to definition of probability ratio of the favorable outcomes i.e the number of getting yellow balls from the bag to the total number of outcomes (balls) gives the probability which is our required answer.

Complete step-by-step answer:
Probability is defined as the ratio of the number of favorable outcomes or chances and the total number of outcomes.
Here,$P(E) = \dfrac{{N(A)}}{{N(S)}}$, where $N(A)$ is number of favorable outcomes and $N(S)$ is the total number of outcomes.
Given, the bag contains 5 red balls and 7 yellow balls.
Hence, the total number of balls in the bag is 12.
The total number of outcomes is 12, as there are 12 balls and a ball is drawn from the bag without looking into the bag.
The favorable number of outcomes is 7, as there are 7 yellows bags in the bag.
For a random event, the probability of an event, say P(E) is defined as the ratio of the number of favorable outcomes or chances and the total number of outcomes.
$P(E) = \dfrac{7}{{12}}$
Therefore, the probability of getting a yellow ball is $\dfrac{7}{{12}}$

Note:The question can also be framed as asking the probability of getting a red ball from the bag.
Given, the bag contains 5 red balls and 7 yellow balls.
Hence, the total number of balls in the bag is 12.
The total number of outcomes is 12, as there are 12 balls and a ball is drawn from the bag without looking into the bag.
The favorable number of outcomes is 5, as there are 5 red balls in the bag.
For a random event, the probability of an event, say P(E) is defined as the ratio of the number of favorable outcomes or chances and the total number of outcomes.
So, $P(E) = \dfrac{5}{{12}}$.Therefore, the probability of getting a red ball is $\dfrac{5}{{12}}$.