An urn contains 4 red, 6 white, and 3 blue marbles. Three marbles are selected at random and without replacement. What is the probability that one of each color is selected? Give your answer as a decimal number, with 3 decimal places.
prob of red, white then blue
= 4/13 * 6/12 * 3/11
prob of red, blue then white
= 4/13 * 3/12 * 6/11
prob of white, red then blue
= 6/13 * 4/12 * 3/11
prob of white, blue then red
= 6/13 *3/12 * 4/11
prob of blue, red then white
=3/13 * 4/12 * 6/11
prob of blue, white then red
= 3/13 * 6/12 * 4/11
NOTE ---- those six ways are all the same probability
numerator = 3*6*4 = 72
denominator = 13 * 12 *11 = 1716
SO
6 (72/1716) = .252
Well, selecting marbles from an urn without replacement is like playing a joke on the marbles. They think they're safe, but little do they know, I'm coming for them!
To determine the probability of selecting one of each color, we need to find the number of successful outcomes divided by the total number of possible outcomes.
The number of successful outcomes would be picking one red, one white, and one blue marble. We can choose one red marble from 4, one white marble from 6, and one blue marble from 3. Therefore, the number of successful outcomes is 4 * 6 * 3 = 72.
Now let's calculate the total number of possible outcomes. We're picking three marbles without replacement, so there are a total of 13 marbles to choose from initially, then 12, and finally 11. Thus, the total number of possible outcomes is 13 * 12 * 11 = 1716.
Finally, we can calculate the probability by dividing the number of successful outcomes by the total number of possible outcomes:
P(one of each color) = successful outcomes / total outcomes = 72 / 1716 ≈ 0.042
So, the probability of selecting one of each color is approximately 0.042. Remember, life is full of surprises, just like selecting marbles from an urn! Keep that sense of humor and let the good times roll!
To find the probability of selecting one marble of each color, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes.
Let's start by calculating the total number of possible outcomes. Since we are selecting three marbles without replacement, the number of possible outcomes is given by the combination formula:
nCr = n! / (r!(n-r)!),
where n is the total number of marbles and r is the number of marbles selected. In this case, n = 13 (4 red + 6 white + 3 blue) and r = 3.
nCr = 13! / (3!(13-3)!) = 13! / (3!10!) = (13 * 12 * 11) / (3 * 2 * 1) = 286.
Therefore, the total number of possible outcomes is 286.
Next, we calculate the number of favorable outcomes. To have one marble of each color, we can first select one red marble, one white marble, and one blue marble. The number of ways to do that is given by:
favorable outcomes = (number of ways to select a red marble) x (number of ways to select a white marble) x (number of ways to select a blue marble).
The number of ways to select a red marble is the number of red marbles available, which is 4. Similarly, the number of ways to select a white marble is 6, and the number of ways to select a blue marble is 3. Therefore:
favorable outcomes = 4 * 6 * 3 = 72.
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
probability = favorable outcomes / total possible outcomes = 72 / 286 = 0.251.
Therefore, the probability that one marble of each color is selected is 0.251 (rounded to 3 decimal places).
To find the probability that one of each color is selected, we need to calculate the total number of outcomes and the number of favorable outcomes.
First, let's find the total number of outcomes. We have a total of 13 marbles in the urn. We will select 3 marbles without replacement, which means that each selection reduces the number of available marbles.
For the first selection, there are 13 marbles to choose from. After the first selection, we have 12 marbles left for the second selection. Finally, for the third selection, we have only 11 marbles remaining.
Next, let's find the number of favorable outcomes, where one of each color is selected.
We can choose one red marble from the 4 available, one white marble from the 6 available, and one blue marble from the 3 available.
So, the number of favorable outcomes is calculated by multiplying the number of choices for each marble color:
4 (red marbles) * 6 (white marbles) * 3 (blue marbles) = 72.
Now we can calculate the probability by dividing the number of favorable outcomes by the total number of outcomes:
Probability = Number of favorable outcomes / Total number of outcomes
= 72 / (13 * 12 * 11)
Calculating this expression gives us the probability as a decimal number. Let's perform the calculation:
Probability = 72 / (13 * 12 * 11) = 0.231 (rounded to 3 decimal places)
Therefore, the probability that one of each color is selected is 0.231.