Answer: The required probability is 4%.
Step-by-step explanation: Given that a large bag of marbles contains equal amounts of 5 colors, red, orange, yellow, green, and blue. Joaquin selects 1 marble then puts it back and selects another.
We are to find the probability of selecting a yellow marble both times.
Let x number of marbles of each color is present in the bag.
Let S be the sample space for the experiment of selecting a marble from the bag.
n(S) = x + x + x + x + x = 5x.
Now, let A denote the event of selecting a yellow marble.
Then, n(A) = x.
Since the second marble is drawn after replacing the first one, so the probability of selecting a yellow marble both times is given by
[tex]P=\dfrac{n(A)}{n(S)}\times \dfrac{n(A)}{n(S)}=\dfrac{x}{5x}\times\dfrac{x}{5x}=\dfrac{1}{25}=\dfrac{1}{25}\times 100\%=4\%.[/tex]
Thus, the required probability is 4%.
