There are 5 yellow, 4 violet, 2 purple, 4 navy, and 4 orange marbles in a hat. You pick 2 marbles from the hat. Marbles are not returned after they have been drawn. Find the probability. Assume that the spinner is separated into equal sections.
P(the first marble is purple and the second marble is not yellow)
19 marbles
p(first is purple) = 2/19
now 18 marbles,
what is p(yellow) first
p(yellow) = 5/18
so
p(NOT yellow) = 13/18
p purple then not yellow) = 2/19 * 13/18
Well, the first thing we need to do is determine the total number of marbles in the hat. Adding up all the different colors, we find that there are a total of 5 + 4 + 2 + 4 + 4 = 19 marbles in the hat.
Now let's determine the number of favorable outcomes (purple on the first draw and not yellow on the second draw) and the number of total outcomes.
For the first draw, there are 2 purple marbles out of the total 19 marbles in the hat. So the probability of drawing a purple marble on the first draw is 2/19.
After the first marble is drawn, it is not returned to the hat. So for the second draw, we have 18 marbles left in the hat. Out of those 18 marbles, there are 19 - 5 = 14 marbles that are not yellow (since the yellow marble was not returned). So the probability of drawing a marble that is not yellow on the second draw is 14/18.
To find the probability of both events occurring, we multiply the probabilities. So the probability that the first marble is purple and the second marble is not yellow is (2/19) * (14/18).
Multiplying these fractions, we find that the probability is approximately 0.0789, or about 7.89%.
To find the probability of the first marble being purple and the second marble not being yellow, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Step 1: Determine the number of favorable outcomes:
We want the first marble to be purple and the second marble to not be yellow. Considering that marbles are not returned after being drawn, the number of favorable outcomes can be calculated as follows:
- First, select 1 purple marble from the 2 available: 2C1 = 2
- Then, select 1 non-yellow marble from the remaining 19 marbles (since there are 5 yellow marbles out of a total of 24 marbles): 19C1 = 19
The total number of favorable outcomes is obtained by multiplying the two results: 2 * 19 = 38.
Step 2: Determine the total number of possible outcomes:
We are drawing 2 marbles from a hat with a total of 24 marbles. So, the total number of ways to select 2 marbles can be calculated as follows:
- Selecting 2 marbles from the 24 available: 24C2 = (24 * 23) / (2 * 1) = 276.
Step 3: Calculate the probability:
The probability is given by the number of favorable outcomes divided by the total number of possible outcomes:
P(the first marble is purple and the second marble is not yellow) = favorable outcomes / total outcomes = 38 / 276.
Thus, the probability of the first marble being purple and the second marble not being yellow is 38/276, which can be simplified if desired.