3/13 = .23 for red marble
2/5 = .40 for blue marble
?? for green marble.
How many fewer than 100?
Probability of both/all events occurring is found by multiplying the probabilities of the individual events.
Express your answer as a common fraction.
2/5 = .40 for blue marble
?? for green marble.
How many fewer than 100?
Probability of both/all events occurring is found by multiplying the probabilities of the individual events.
To begin with, the probability of selecting a green marble at random is unknown. However, let's give it a name for now and call it "G." Moving on to the second selection, the probability of choosing a red marble, given that we've already grabbed a green one, is 2/12 since there is one fewer marble and two fewer red marbles.
Now, to calculate the probability of selecting a green marble and then a red marble, we multiply the two probabilities together:
(G probability) x (R probability) = (unknown probability) x (2/12).
Now, we know that the probability of selecting a green marble and then a red marble is 3/13. Therefore, we can set up the equation:
(unknown probability) x (2/12) = 3/13.
To find the unknown probability, we isolate it by dividing both sides of the equation by 2/12:
(unknown probability) = (3/13) / (2/12).
= (3/13) x (12/2).
= (3/13) x 6.
= 9/13.
So, the probability of selecting, at random and without replacement, a green marble and then a red marble from the bowl is 9/13. Hope that brings a smile to your face!
First, let's find the probability of selecting a green marble. We are given that the probability of selecting a red marble is 3/13 and the probability of selecting a blue marble is 2/5. Therefore, the probability of selecting a green marble can be found by subtracting the sum of these two probabilities from 1 (since the total probability of selecting a marble must equal 1).
Probability of selecting a green marble = 1 - (Probability of selecting a red marble + Probability of selecting a blue marble)
Probability of selecting a green marble = 1 - (3/13 + 2/5)
To simplify the expression, we need to find a common denominator for 13 and 5, which is 65.
Probability of selecting a green marble = 1 - (15/65 + 26/65)
Probability of selecting a green marble = 1 - (41/65)
Probability of selecting a green marble = 24/65
Now that we have the probability of selecting a green marble, we need to find the probability of selecting a red marble next. Since we are selecting without replacement, the number of marbles in the bowl reduces by one after the first selection.
Probability of selecting a green marble and then a red marble = probability of selecting a green marble × probability of selecting a red marble (after the green marble is selected)
Probability of selecting a green marble and then a red marble = (24/65) × (3/12)
To simplify this expression, we can cancel out the common factors:
Probability of selecting a green marble and then a red marble = (2/5) × (1/4)
Probability of selecting a green marble and then a red marble = 2/20
Probability of selecting a green marble and then a red marble = 1/10
Therefore, the probability of selecting a green marble and then a red marble from the bowl on the first two selections is 1/10.