Question

A bag has 9 red marbles and 6 green marbles. How do you find the probability of drawing a green marble, replacing it, and drawing another green marble?

Answer 1

Hint: Here we need to find the value of the probability of drawing green balls. We will first count the total number of balls by adding the number of both the marbles. Then we will find the probability of drawing the green ball from the bag which will be equal to the ratio of the number of green balls to the total number of balls. After replacing the green balls, the number of green balls remains the same. Then after replacing the green ball, we will again find the probability of drawing the green balls.

Complete step by step solution:
Here we need to find the value of the probability of drawing green balls.
It is given that
Number of green balls \[ = 6\]
Number of red balls \[ = 9\]
Therefore, the total number of balls is equal to the sum of red balls and green balls.
Total number of balls \[ = 9 + 6 = 15\]
Now, we will find the probability of drawing the green ball which will be equal to the ratio of the number of green balls to the total number of balls.
Probability of drawing the green ball \[ = \dfrac{6}{{15}}\]
Now, we will further reduce the obtained fraction.
\[ \Rightarrow \] Probability of drawing the green ball \[ = \dfrac{2}{5}\]
As it is given that the green ball drawn has replaced the bag again. So the total number of balls remains the same and also the total number of green balls also remains the same.
Therefore, probability of drawing the green ball again \[ = \dfrac{6}{{15}}\]
Now, we will further reduce the obtained fraction. So, dividing the numerator and denominator by 3, we get
\[ \Rightarrow \] Probability of drawing the green ball \[ = \dfrac{2}{5}\]
As both these requirements need to be fulfilled, so the required probability will be the multiplication of both.
Required probability \[ = \dfrac{2}{5} \times \dfrac{2}{5}\]
On multiplying the fractions, we get
\[ \Rightarrow \] Required probability \[ = \dfrac{4}{{25}}\]

Hence, the required probability of drawing the green ball is equal to \[\dfrac{4}{{25}}\].

Note:
Probability tells us the extent to which an event is likely to occur, i.e. the possibility of the occurrence of an event. Hence, it is measured by dividing the favorable outcomes by the total number of outcomes. The probability of an event varies from 0 to 1 that is it cannot be less than 0 or greater than 1. If the probability is 1 then the event is called a sure event, whereas the event with 0 probability never occurs. We need to keep in mind that when we replace the ball again with the bag then the total number will become equal to the initial number of balls. So the probability of drawing the ball from the bag will remain the same.