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 $(\frac{1}{9})$.

Step-by-step 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

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

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

The probability of picking second  blue bean in SECOND ATTEMPT

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

So, the combined probability =  $(\frac{1}{3} ) \times(\frac{1}{3} ) = (\frac{1}{9} )$

Hence, probability of getting a blue jelly bean both times is $(\frac{1}{9})$.