Question

A fish tank has a certain number of males and a higher number of females. An equal number of male and female fish are then added to the tank. Does the probability of randomly picking a male fish a. go up, b. go down, c. stay the same, d. we can't tell?

Answer 1

option a

Explanation:

We can look at this by first finding the probability of picking a male before the extra animals were added, then finding it after the addition.

To make it more concrete, let's say there are 10 males and 20 females at the start. This means that the probability of randomly picking a male is:

`10/(10+20)=10/30=1/3=.bar3`

Now let's add 10 males and 10 females. What is the probability now?

`20/(20+30)=20/50=4/10=.4`

The probability went up. Why? Because we added male animals in a ratio higher than in the original population.

Is this always the case? Let's work a different example to show that it is. Instead of having a set number of males and females, let's use `x` to represent the multiples we're working with. We're told there are `x` males and `2x` females at the start. The probability of randomly picking a male is therefore:

`x/(x+2x)=x/(3x)=1/3=.bar3`