a) 0.1563
b) 0.1667
Step-by-step explanation:
a)
Inside the bag of the problem, we have:
r = 5 (number of red marbles)
g = 8 (number of green marbles)
b = 3 (number of blue marbles)
In this part, we replace the first marble before drawing the second.
Here we want to find the probability of selecting a red, then a green marble.
The total number of marbles is
n = r + g + b = 5 + 8 + 3 = 16
So, the probability of drawing a red marble at the 1st attempt is
Then, the first marble is replaced back into the bag before making the second draw.
The probability of drawing a green marbles at the second draw is therefore
Since the two events are independent, the combined probability of selecting a red, then a green marble is:
b)
In this second experiment, we do not replace the first marble before drawing the second one.
As in part a), the probability of drawing a red marble at the 1st draw is
Now, the situation changes. In fact, we do not put back the red marble into the bag. Therefore, at the second draw, the number of balls inside the bag is
And so ,the probability of drawing a green marbles at the second draw is
As before, the two events are independent, so the combined probability of selecting a red, then a green marble is: