Find each probability if you pick one marble, replace it, then pick a second marble. P(black, white) The bag contains 1 black, 2 white and 3 striped.
Well, let's see...the probability of picking a black marble on the first draw is 1/6 and the probability of picking a white marble on the second draw is 2/6 (since we replaced the first marble). So, the probability of picking a black marble, then a white marble is (1/6) * (2/6), which is 1/18.
But you know, striped marbles probably have a different sense of fashion, so they might not appreciate being left out of the probability equation. Let's include them too! The probability of picking a striped marble on the first draw is 3/6, and the probability of picking a white marble on the second draw is still 2/6. So, the probability of picking a striped marble, then a white marble is (3/6) * (2/6), which simplifies to 1/6.
In conclusion, the probability of picking a black marble, then a white marble is 1/18, and the probability of picking a striped marble, then a white marble is 1/6. Now, that's a colorful combination!
To find the probability of picking a black marble followed by a white marble with replacement, we can use the formula:
P(black, white) = P(black) * P(white|black)
Given that the bag contains 1 black, 2 white, and 3 striped marbles, we can calculate:
P(black) = (Number of black marbles)/(Total number of marbles) = 1/6
P(white|black) = (Number of white marbles)/(Total number of marbles) = 2/6
Substituting the values:
P(black, white) = (1/6) * (2/6) = 2/36 = 1/18
Therefore, the probability of picking a black marble followed by a white marble with replacement is 1/18.
To find the probability of picking one black marble and one white marble when replacing the first marble, you need to consider the total number of marbles and the number of black and white marbles in the bag.
Step 1: Find the probability of picking a black marble on the first pick.
The bag contains a total of 1 black marble, 2 white marbles, and 3 striped marbles. So, there are 6 marbles in total.
The probability of picking a black marble on the first pick is given by:
P(black) = Number of black marbles / Total number of marbles
= 1 / 6
Step 2: As it is mentioned that the marble is replaced after the first pick, the probability of picking a white marble on the second pick is the same as the probability of picking a black marble on the first pick.
So, the probability of picking a white marble on the second pick is also:
P(white) = 1 / 6
Step 3: To find the probability of both events happening together (picking one black marble and then picking one white marble), you need to multiply the probabilities of each event happening separately:
P(black, white) = P(black) * P(white)
= (1 / 6) * (1 / 6)
= 1 / 36
Therefore, the probability of picking one black marble, replacing it, and then picking one white marble is 1/36.
1/6 for black or 17%
1/3 for wahite or 33%
1/2 for striped or 50%