Question

A bag has 5 red marbles, 6 blue marbles and 4 black marbles. What is the probability of picking a red marble, replacing it, and then picking another red marble?

Answer 1

There are 15 marbles in the bag. This gives us the probability of picking a red marble as 5/15, or 1/3. Because you replace the marble therefore making the probability the same each time, and as it's a logical 'and' operation, you multiply the probabilities like this:
(1/3)•(1/3)=(1/3)^2

Because (a/b)^c = a^c/b^c, P(two red marbles) = 1^2/3^2 = 1/9.

Answer 2

$\frac{1}{9}$

Working;
The probability of picking a red is $\frac{5}{15}$

The probability remains the same for the second picking since there is replacement;
A red followed by a red is;
$\frac{5}{15} * \frac{5}{15} = \frac{1}{9}$