Question

Jada is allergic to cats so she has decided to get a couple of pet fish. There are 10 fantail goldfish and 9 calico goldfish in a tank at the store. Jada tells the pet store employee that she will take the first two fish he catches. The employee dips in a net and catches one fish, puts it in a bag of water for Jada, and then catches a second fish in the same manner. What is the probability Jada ends up with two calico goldfish?

Answer 1

Solution

We are given

10 Fantail goldfish

9 Calico goldfish

We want to find the probability that Jada ends up with two calico goldfish

This is a probability that is without replacement

Total number of goldfish = 10 + 9 = 19

Probability (p) of Catching the first calico goldfish

$\begin{gathered} p=\frac{\text{required outcome}}{total\text{ outcome}} \\ p=\frac{9}{10+9} \\ p=\frac{9}{19} \end{gathered}$

Now, we will be left with

10 fantail goldfish and 8 calico goldfish

Probability (p) of Catching the second calico goldfish

Probability that Jada ends up with two calico goldfish

$\begin{gathered} p=\frac{9}{19}\times\frac{8}{18} \\ p=\frac{4}{19} \end{gathered}$

The probability is 4