Question

There is a bag filled with 6 blue and 5 red marbles. A marble is taken at random from the bag, the colour is noted and then it is replaced. Another marble is taken at random. What is the probability of getting exactly 1 red?

Answer 1

The probability of getting exactly 1 red is $\dfrac{60}{121}$.

Given information:

There is a bag filled with 6 blue and 5 red marbles.

A marble is taken at random from the bag, the colour is noted and then it is replaced. Another marble is taken at random.

It is required to find the probability of getting exactly one red marble.

Now, the red marble can occur on the first draw or the second draw.

The probability of getting exactly 1 red marble from the first draw will be,

$P(1)=\dfrac{5}{11}\times \dfrac{6}{11}\\P(1)=\dfrac{30}{121}$

The probability of getting exactly 1 red marble from the second draw will be,

$P(2)=\dfrac{6}{11}\times \dfrac{5}{11}\\P(2)=\dfrac{30}{121}$

So, the total probability of the event will be,

$P=P(1)+P(2)\\P=\dfrac{30}{121}+\dfrac{30}{121}\\P=\dfrac{60}{121}$

Therefore, the probability of getting exactly 1 red is $\dfrac{60}{121}$.

For more details, refer to the link:

https://brainly.com/question/21245386