A bag of marbles contains 3 yellow marble, 3 red marbles, and 5 green marbles. If a marble is chosen, put back in the bag and then a second marble is chosen, what is the probability that both marbles will be red?
I think it is 2 red 10 all together 2:10
2/10 = 1/5
But I am not sure because it says both marbles will be red.
CORRECTION ON THE QUESTION:
THE QUESTION WAS SUPPOSE TO SAY 2 RED MARBLES, NOT 3 RED MARBLES
SEE CORRECT QUESTION BELOW,
A bag of marbles contains 3 yellow marble, 2 red marbles, and 5 green marbles. If a marble is chosen, put back in the bag and then a second marble is chosen, what is the probability that both marbles will be red?
I think it is 2 red 10 all together 2:10
2/10 = 1/5
But I am not sure because it says both marbles will be red.
CORRECTION THE 1ST QUESTION WAS SUPPOSE TO SAY 2 RED MARBLES NOT 3 RED MARBLES.
Since you are putting the marble back, the prob of the second event is the same as the first one.
Prob(red,red) = (2/10(2/10)
= 1/25
To find the probability of both marbles being red, we need to consider the total number of possible outcomes and the number of favorable outcomes.
First, let's determine the total number of possible outcomes. We have a bag with a total of 11 marbles (3 yellow, 3 red, and 5 green). When we choose a marble and put it back, we are essentially conducting independent events or trials. In this case, since we choose a marble, put it back, and then choose another marble, we have two trials.
For each trial, the number of possible outcomes is equal to the total number of marbles in the bag, which is 11. Therefore, the total number of possible outcomes for both trials is 11 multiplied by 11, which is equal to 121.
Next, let's determine the number of favorable outcomes. We want both marbles to be red. Since we are replacing the chosen marble in the bag before the second draw, the probability of drawing a red marble remains the same for both trials.
The number of red marbles in the bag is 3. Therefore, the number of favorable outcomes for the first trial (drawing a red marble) is 3, and the number of favorable outcomes for the second trial (drawing another red marble) is also 3.
To find the total number of favorable outcomes for both trials, we multiply the number of favorable outcomes for each trial. In this case, 3 multiplied by 3 equals 9.
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes.
So, the probability of drawing two red marbles is 9/121.