what's the decimal Be sure you are writing out your steps. You will have to submit your shown work for each problem at the end A box contains three red marbles and six blue marbles. What is the probability of selecting at random, without replacement, two blue marbles? (1 point) Responses 49 4 ninths 112 1 over 12 512 5 over 12 19
First, we need to calculate the probability of selecting a blue marble on the first draw. This can be calculated by dividing the number of blue marbles by the total number of marbles:
P(First draw is blue) = Number of blue marbles / Total number of marbles
P(First draw is blue) = 6 / (6 + 3)
P(First draw is blue) = 6 / 9
P(First draw is blue) = 2 / 3
Since we are drawing without replacement, after drawing one blue marble, there will be 5 blue marbles left and a total of 8 marbles left. Therefore, the probability of selecting a second blue marble is:
P(Second draw is blue) = Number of remaining blue marbles / Total number of remaining marbles
P(Second draw is blue) = 5 / 8
To find the overall probability of selecting two blue marbles, we multiply the probabilities of the two events:
P(Selecting two blue marbles) = P(First draw is blue) * P(Second draw is blue)
P(Selecting two blue marbles) = 2/3 * 5/8
P(Selecting two blue marbles) = 10 / 24
P(Selecting two blue marbles) = 5 / 12
So, the probability of selecting at random, without replacement, two blue marbles is 5/12 or 5 over 12.