19. you choose one marble from the bag below, do not replace it, then pick a second marble. what is the…

Explanation:

Step1: Calculate probability of first - pick

There are 2 blue marbles and 8 total marbles. The probability of picking a blue marble first is the number of blue marbles divided by the total number of marbles. $P(\text{blue first})=\frac{2}{8}=\frac{1}{4}$

Step2: Calculate probability of second - pick

After picking a blue marble first (without replacement), there are 7 marbles left and 3 green marbles. The probability of picking a green marble second is the number of green marbles divided by the remaining number of marbles. $P(\text{green second}|\text{blue first})=\frac{3}{7}$

Step3: Calculate joint probability

By the multiplication rule for dependent events $P(A\cap B)=P(A)\times P(B|A)$. Here, $A$ is the event of picking a blue marble first and $B$ is the event of picking a green marble second. $P(\text{blue first and green second})=\frac{1}{4}\times\frac{3}{7}=\frac{3}{28}$

Answer:

$\frac{3}{28}$