Answer:
[tex]\frac{5}{96}[/tex]
Step-by-step 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:
[tex]n=5+6+8+5=24[/tex]
The number of yellow beans at the beginning is
[tex]y=6[/tex]
Therefore, the of selecting a yellow jellybean at the beginning is
[tex]p(y)=\frac{y}{n}=\frac{6}{24}=\frac{1}{4}[/tex]
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
[tex]p=5[/tex]
So, the probability of selecting a purple bean at the 2nd attempt is
[tex]p(p)=\frac{5}{24}[/tex]
Therefore, the combined probability of selecting a yellow jellybean followed by a purple one is
[tex]p(yp)=p(y)\cdot p(p)=\frac{1}{4}\cdot \frac{5}{24}=\frac{5}{96}[/tex]
