The theoretical probability to draw a black marble is 0.23.
Step-by-step explanation:
First add up the total amount of marbles in the bag.
14 gray marbles + 7 black marbles + 10 white marbles = 31 total marbles.
Since we need the odds of a black marble being drawn, divide 7 (the amount of black marbles) by 31 (the amount of total marbles).
7/31 ---> 0.22580645161 (it is easiest to use a calculator on this step)
Lastly, round the decimal to the nearest hundredth.
0.22580645161 ---> 0.23
0.23 would be the odds of drawing a black marble.