Question

Suppose you have a bag containing 2 black marbles and 3 red marbles. You reach into the bag, select a marble, see what color it is and replace it in the bag. Then you repeat this process a second time. What is the probability of picking a red marble both times?

Answer 1

`(9)/(25)`

Explanation:

Given that the bag contains black and red marbles.

Number of black marbles in the bag = 2

Number of red marbles in the bag = 3

Total number of marbles in the bag = Number of black marbles + Number of red marbles = 2 + 3 = 5

Let us have a look at the formula for probability of an event E, which can be observed as:

`P(E) = \frac{\text{Number of favorable cases}}{\text {Total number of cases}}`

`P(\text{First red marble}) = \frac{\text{Number of red marbles}}{\text{Total number of marbles}} = (3)/(5 )`

Now, the marble chosen at first is replaced.

Therefore, the count remains the same.

`P(\text{Second red marble}) = \frac{\text{Number of red marbles}}{\text{Total number of marbles}} = (3)/(5)`

Now, the required probability can be found as:

`P(\text{First red marble})* P(\text{Second red marble}) = (3)/(5)* (3)/(5) = \bold{(9)/(25) }`