Question

a jar of an unknown amount of red, blue, and yellow marbles sits before you. marbles are put back into the jar before the next random pull. what is the probability of pulling a red marble?

Explanation:

Step1: Count the number of each color marbles

Assume there are \(r\) red marbles, \(b\) blue marbles, \(y\) yellow marbles. The total number of marbles \(n=r + b + y\).

Step2: Use the probability formula

The probability \(P\) of pulling a red marble is \(P=\frac{r}{n}\). But since we can't count directly, we use experimental probability. If we run a large - number of trials (say \(N = 100\) trials). Let the number of times we pull a red marble be \(M\). Then the experimental probability \(P=\frac{M}{N}\).
If we assume after running \(100\) trials (by clicking the "Run Trial × 100" button), and assume we get the number of red - marble pulls. But if we just estimate from visual (counting the proportion of red marbles in the jar), assume there are 9 red marbles, 11 blue marbles and 10 yellow marbles (\(n=9 + 11+10=30\)). Then \(P=\frac{9}{30}=0.3\) (this is wrong assumption). But if we use the given options and assume a better visual - count: assume red marbles are about 9, total marbles about 20. \(P = 45\%\) (a rough visual estimate as red marbles seem to be less than half but not too less).

Answer:

45%