A bag contains 8 red, 12 white and 4 blue marbles. If 2 marbles are selected in succession (without replacement), find the probability as a common fraction in simplest form that first is red and second is blue
first red = 8/24
second blue = 4/23
so
(1/3)(4/23) = 4/69
The Answer is The Probality of picking a Black Marble from the Bah is 0.06
To find the probability of drawing a red marble followed by a blue marble, we need to calculate the probability of each event and multiply the probabilities together since the events are happening in succession without replacement.
First, let's calculate the probability of drawing a red marble:
There are a total of 24 marbles in the bag initially, with 8 of them being red. So, the probability of drawing a red marble on the first draw is:
P(red on 1st draw) = Number of red marbles / Total number of marbles
= 8 / 24
= 1/3.
After successfully drawing a red marble on the first draw, there will be one fewer red marble and 23 total remaining marbles. Now, let's calculate the probability of drawing a blue marble on the second draw:
There are now only 4 blue marbles left out of the 23 total remaining marbles. So, the probability of drawing a blue marble on the second draw after a red marble was drawn on the first draw is:
P(blue on 2nd draw) = Number of blue marbles / Total remaining marbles
= 4 / 23.
Now, we multiply the probabilities together to get the overall probability:
P(red then blue) = P(red on 1st draw) * P(blue on 2nd draw)
= (1/3) * (4/23)
= 4/69.
Therefore, the probability of drawing a red marble first and then a blue marble from the bag is 4/69 as a common fraction in simplest form.
To find the probability that the first marble selected is red and the second marble selected is blue, we need to calculate the probability of each event happening and then multiply them together.
First, let's calculate the probability of selecting a red marble as the first one.
We have a total of 8 red marbles out of a total of 8 + 12 + 4 = 24 marbles. Therefore, the probability of selecting a red marble as the first one is 8/24.
Next, let's calculate the probability of selecting a blue marble as the second one, given that the first marble was red.
After selecting the red marble, there are now 23 marbles left in the bag, with 4 blue marbles remaining. Therefore, the probability of selecting a blue marble as the second one, given that the first marble was red, is 4/23.
To find the overall probability, we multiply the probabilities of the two events:
(8/24) * (4/23) = 32/552 = 8/138
So, the probability that the first marble selected is red and the second marble selected is blue is 8/138 in simplest form.