A bag contains 3 blue marbles, 4 red marbles, and 2 white marbles. Three times you draw a marble and return it. Find the probability.
P(all white)
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
(2/9)^3 = ?
To find the probability of drawing all white marbles, we need to calculate the ratio of the number of favorable outcomes (drawing all white marbles) to the total number of possible outcomes.
1. Determine the total number of possible outcomes:
In this case, we are drawing marbles three times, and each time we return the marble back to the bag. Therefore, the total number of possible outcomes for each draw is the total number of marbles in the bag, which is 9 (3 blue + 4 red + 2 white).
2. Determine the number of favorable outcomes:
To calculate the number of favorable outcomes, we need to determine the probability of drawing a white marble on each of the three draws and multiply them together.
The probability of drawing a white marble on the first draw is 2/9 (since there are 2 white marbles out of 9 total marbles).
Similarly, the probability of drawing a white marble on the second and third draws is also 2/9.
So, the number of favorable outcomes is calculated by multiplying the probabilities of the three draws together: (2/9) * (2/9) * (2/9) = (8/729).
3. Calculate the probability:
Finally, to find the probability of drawing all white marbles, we divide the number of favorable outcomes by the total number of possible outcomes:
P(all white) = (number of favorable outcomes) / (total number of possible outcomes)
= (8/729) / 1
= 8/729
Therefore, the probability of drawing all white marbles is 8/729.