Answer to Question #251080 in Statistics and Probability for IDK

Question

There is a bag filled with 4 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 2 of the same colour?

Answer 1

There are total 9 marbles, out of which there are 4 blue and 5 red marbles.

Probability of getting blue marbles in first turn will be $\frac{4}{9}$ .

Now, since the ball is replaced, the probability of again getting the blue ball will be same equal to $\frac{4}{9}$

Now, from the multiplication theorem of probability, the probability of getting 2 blue balls will be:

$\frac{4}{9}\times\frac{4}{9}=\frac{16}{81}$