Question

Suppose I pick a jelly bean at random from a box containing eight red and four blue ones. I record the color and put the jelly bean back in the box.What is the probability of getting a blue jelly bean both times if I do this twice?

Answer 1

The probability of choosing a blue jelly bean in both attempts is
`((1)/(9))`.

Explanation:

Here, the total number of red beans = 8

The total number of blue beans = 4

The total beans in the bag = 8 + 4 = 12 beans

Now, probability of picking first blue bean in FIRST ATTEMPT

`= \frac{\textrm{Total Blue Beans in Bag}}{\textrm{Total Beans in Bag}} = (4)/(12) = ((1)/(3) )`

As given, the picked bean in replaced inside the bag.

The probability of picking second blue bean in SECOND ATTEMPT

`= \frac{\textrm{Total Blue Beans in Bag}}{\textrm{Total Beans in Bag}} = (4)/(12) = ((1)/(3) )`

So, the combined probability =
`((1)/(3) ) *((1)/(3) ) = ((1)/(9) )`

Hence, probability of getting a blue jelly bean both times is
`((1)/(9))`.