PLEASE HELP!!! THERE IS A PICTURE ATTACHED
Francisco is playing a game with 3 green, 2 yellow, 4 red, and 3 black marbles in a bag. He has calculated the probability of drawing a yellow marble, not replacing it, and then drawing a red marble. Explain the error in his solution.(the picture is Fransisco's work)

ample Response: The events are dependent, so the sample space changes for the second draw. After drawing the first marble, there are only 11 marbles left. The probability is (
2
12
) (
4
11
) =
8
132
, or
2
33
. ;

Answered by MissLorwee | 2024-06-11

Well, the problem is that he does not replace the first marble after he draws it. Therefore, yes, he has a 2/12 probability of drawing a yellow marble first, but then he has a 4/11 probability of drawing a red marble second, not 4/12. This is because there are going to only be 11 marbles left in the bag after he draws the first marble and does not replace it.
The correct answer would be: (2/12)(4/11)=8/132=4/66=2/33

Answered by bjboss | 2024-06-24

To find the probability of drawing a yellow marble and then a red marble without replacement, you first calculate the probability of each event separately, adjusting the total number of marbles after the first draw. The correct final probability is 33 2 ​ . Francisco may have erred by not considering the change in total marbles after the first draw.
;

Answered by MissLorwee | 2024-09-05