Question

question 5 of 5 a jar contains 16 marbles, each of which is a solid color. there are 9 red marbles and 7 white marbles. colby will draw one marble at random and then, without replacing it, will draw another marble from the jar at random. which of the following expressions shows the probability of colby drawing 2 white marbles? a. $\frac{7}{16}cdot\frac{3}{16}$ b. $\frac{7}{16}cdot\frac{6}{15}$ c. $\frac{8}{15}+\frac{9}{16}$ d. $\frac{8}{15}cdot\frac{9}{16}$

Explanation:

Step1: Calculate first - draw probability

The probability of drawing a white marble on the first draw is the number of white marbles divided by the total number of marbles. There are 7 white marbles and 16 total marbles, so the probability of the first - draw being white is $\frac{7}{16}$.

Step2: Calculate second - draw probability

After the first white marble is drawn without replacement, there are 6 white marbles left and 15 total marbles left. So the probability of drawing a white marble on the second draw is $\frac{6}{15}$.

Step3: Calculate combined probability

Since these are independent events in the sense of sequential non - replacement draws, the probability of both events occurring is the product of their individual probabilities. So the probability of drawing 2 white marbles is $\frac{7}{16}\times\frac{6}{15}$.

Answer:

B. $\frac{7}{16}\cdot\frac{6}{15}$