A bag contains
4
white marbles,
5
red marbles, and
9
blue marbles.
If a marble is drawn from the bag, replaced, and another marble is drawn, what is the probability of drawing first a white marble, and then a blue marble?
A bag contains
5
green marbles,
9
blue marbles, and
4
red marbles.
If two different marbles are drawn from the bag, what is the probability of drawing first a green marble and then a red marble?
1.
prob(white, then blue) = (4/18)(9/18) = 1/9 , with the first marble returned.
2. assuming the first marble is not returned
prob(green, then red) = (5/18)(4/17) = 10/153
To calculate the probability of both events occurring, we need to multiply the probabilities of each event happening individually.
First Question:
Given a bag with 4 white marbles, 5 red marbles, and 9 blue marbles, the total number of marbles is 4 + 5 + 9 = 18.
The probability of drawing a white marble on the first draw is 4/18.
Since we replace the marble after drawing, the total number of marbles remains 18 for the second draw.
The probability of drawing a blue marble on the second draw is 9/18.
To find the probability of both events happening, we multiply the probabilities:
(4/18) * (9/18) = 36/324 = 1/9.
Therefore, the probability of drawing first a white marble and then a blue marble is 1/9.
Second Question:
Given a bag with 5 green marbles, 9 blue marbles, and 4 red marbles, the total number of marbles is 5 + 9 + 4 = 18.
The probability of drawing a green marble on the first draw is 5/18.
After the first draw, we are left with 17 marbles (since we do not replace the marble).
The probability of drawing a red marble on the second draw is 4/17.
To find the probability of both events happening, we multiply the probabilities:
(5/18) * (4/17) = 20/306 = 10/153.
Therefore, the probability of drawing first a green marble and then a red marble is 10/153.
To find the probability of drawing a certain sequence of marbles, we need to compute the probability of each individual event and then multiply them together.
For the first question:
1. Calculate the probability of drawing a white marble first: There are a total of 18 marbles in the bag, and 4 of them are white. Therefore, the probability of drawing a white marble is 4/18.
2. Since the marble is replaced before the second draw, the probabilities for each draw are independent. So, the probability of drawing a blue marble after drawing a white marble is also 9/18.
3. To find the probability of both events happening, multiply the two probabilities together: (4/18) * (9/18) = 36/324 = 1/9. Therefore, the probability of drawing first a white marble and then a blue marble is 1/9.
For the second question:
1. Calculate the probability of drawing a green marble first: There are a total of 18 marbles in the bag, and 5 of them are green. Therefore, the probability of drawing a green marble is 5/18.
2. After the first draw, the total number of marbles decreases to 17. Since we are drawing a different marble, there are now 4 red marbles remaining. Therefore, the probability of drawing a red marble after drawing a green marble is 4/17.
3. Multiply the two probabilities together: (5/18) * (4/17) = 20/306 = 10/153. Therefore, the probability of drawing first a green marble and then a red marble is 10/153.