Question

A jar contains 5 purple, 6 yellow, 8 green, and 5 orange jellybeans. What is the probability of selecting a yellow jellybean followed by a purple one, with replacement?

Answer 1

`(5)/(96)`

Explanation:

At the beginning, the jar contains the following beans:

5 purple

6 yellow

8 green

5 orange

Therefore, the total number of jellybeans in the jar tha beginning is:

`n=5+6+8+5=24`

The number of yellow beans at the beginning is

`y=6`

Therefore, the of selecting a yellow jellybean at the beginning is

`p(y)=(y)/(n)=(6)/(24)=(1)/(4)`

After selecting this yellow bean, the yellow bean it is replaced in the jar, so the number of total beans is still n = 24.

And the number of purple beans inside is

`p=5`

So, the probability of selecting a purple bean at the 2nd attempt is

`p(p)=(5)/(24)`

Therefore, the combined probability of selecting a yellow jellybean followed by a purple one is

`p(yp)=p(y)\cdot p(p)=(1)/(4)\cdot (5)/(24)=(5)/(96)`