A box contains 3 red marbles, 6 blue, and 1 white. The marbles are selected at random, one at a time, and are not replaced. Find the probability.
10. P (red and white and blue).
If you want the specific order, RWB, then it is
(3/10)(1/9)(6/8) = 1/40
If the order of the red, white and blue does not matter, the prob = 6(1/40 ) = 3/20
To find the probability of selecting one red marble, one white marble, and one blue marble from the box without replacement, we need to calculate the individual probabilities of each event and then multiply them together.
Step 1: Determine the total number of marbles in the box.
There are a total of 3 red marbles + 6 blue marbles + 1 white marble = 10 marbles.
Step 2: Calculate the probability of selecting a red marble first.
The probability of selecting a red marble is 3 red marbles / 10 total marbles = 3/10.
Step 3: Calculate the probability of selecting a white marble second.
Since we are not replacing the marble, after selecting a red marble, there will be a total of 9 marbles left in the box, and 1 of them will be white.
Therefore, the probability of selecting a white marble second is 1 white marble / 9 remaining marbles = 1/9.
Step 4: Calculate the probability of selecting a blue marble third.
After selecting a red marble and a white marble, there will be a total of 8 marbles left in the box, and 6 of them will be blue.
Therefore, the probability of selecting a blue marble third is 6 blue marbles / 8 remaining marbles = 6/8 = 3/4.
Step 5: Multiply the probabilities together.
The probability of selecting a red marble, a white marble, and a blue marble in that order is:
(3/10) * (1/9) * (3/4) = 9/360 = 1/40.
So, the probability of selecting a red and a white and a blue marble from the box without replacement is 1/40.
To calculate the probability of selecting a red, white, and blue marble from the box, you need to consider the number of possible outcomes and the number of favorable outcomes.
First, let's calculate the total number of possible outcomes. Since the marbles are selected without replacement, the total number of marbles decreases each time a marble is chosen. The initial total number of marbles is 3 (red) + 6 (blue) + 1 (white) = 10.
Now, let's calculate the number of favorable outcomes. To pick a red marble, you have 3 options. After choosing a red marble, you have 2 red marbles left. To pick a white marble, you have 1 option. After picking a white marble, there are no more white marbles left. Finally, to pick a blue marble, you have 6 options.
So, the number of favorable outcomes is 3 * 1 * 6 = 18.
Therefore, the probability of selecting a red, white, and blue marble is:
P(red and white and blue) = Number of favorable outcomes / Number of possible outcomes
= 18 / 10
= 9 / 5
= 1.8
So, the probability of selecting a red, white, and blue marble is 1.8 or 9/5.