Question

a bowl contains 6 blue and four red marbles. Three random picks are to be made from the bowl in the following fashion: for each pick, a marble is selected and its color is recorded. It is then returned to the jar along with an additional marble of the same color. Determine the probability that a red marble is selected on each of the three picks?

Answer 1

The probability of picking a red marble 3 times in a row  = $(\frac{8}{125})$

Step-by-step explanation:

Here, the total number of red marbles  =  4

The total number of blue marbles  = 6

Now, as the Repetition is allowed.

Let E: The event of picking a red marble

$P(E) = \frac{\textrm{The total number of red marbles}}{\textrm{Total marbles}}$

So, $P(E) = \frac{4}{10} = \frac{2}{5}$

Now, as we know after first picking, the chosen red marble is REPLACED in the bowl.

So, again the bowl has 4 red marbles and 10 in total.

⇒P(picking a red marble again)  = 2/5

And similarly for the third time.

So, the probability of picking a red marble 3 times in a row  = $(\frac{2}{5}) \times (\frac{2}{5})\times (\frac{2}{5}) = \frac{8}{125}$