Question

This is to do with independant events & probability trees

There is a bag filled with 3 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 reds?

Answer 1

Answer: The probability of getting two red marbles is P = 0.141

Explanation:

We know that in the bag there are 3 blue marbles and 5 red marbles, then there is a total of 8 marbles in the bag.

The probability of taking at random a red marble is equal to the quotient between the number of red marbles and the total number of marbles, this is:

p = 3/8

Suppose we got a red marble:

Now we replace the red marble we took, so in the bag there are again 3 red marbles and 8 total marbles, then the probability of getting another red marble is again:

q = 3/8

The joint probability (this is, the probability of both events happening) is equal to the product of the individual probabilities, with gives us:

P = p*q = (3/8)*(3/8) = 9/64 = 0.141