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

Answer:

$\frac{5}{96}$

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:

$n=5+6+8+5=24$

The number of yellow beans at the beginning is

$y=6$

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

$p(y)=\frac{y}{n}=\frac{6}{24}=\frac{1}{4}$

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

$p(p)=\frac{5}{24}$

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

$p(yp)=p(y)\cdot p(p)=\frac{1}{4}\cdot \frac{5}{24}=\frac{5}{96}$