A jar contains four blues marbles and two green marbles. Without looking, two marbles are drawn from the jar. What is the probability that two marbles with the same color will be selected?

Either two blues or two greens

prob of 2 blues = (4/6)(3/5) = 2/5
prob of 2 grees = (2/6)(1/5) = 1/15 , this is where PsyDAG slipped up

so prob of 2 of same colour = 2/5 + 1/15 = 7/15

Why do u multiply by 3/5 and 1/5

⁄Mia Culpa! Sorry.

To find the probability of drawing two marbles of the same color, we need to first determine the total number of possible outcomes and the number of favorable outcomes.

The total number of possible outcomes is the number of ways we can draw two marbles from a jar containing a total of six marbles. This can be calculated using the combination formula:

nCr = n! / r!(n - r)!

In this case, n (the total number of marbles) is 6 and r (the number of marbles drawn) is 2. So, the total number of possible outcomes is:

6C2 = 6! / 2!(6 - 2)! = 6! / 2!4! = (6 * 5 * 4 * 3 * 2 * 1) / (2 * 1 * 4 * 3 * 2 * 1) = 15

Next, we need to determine the number of favorable outcomes, which is the number of ways we can draw two marbles of the same color. Since there are four blue marbles and two green marbles, we have two possibilities: drawing two blue marbles or drawing two green marbles.

The number of ways to draw two blue marbles is given by:

4C2 = 4! / 2!(4 - 2)! = 4! / 2!2! = (4 * 3 * 2 * 1) / (2 * 1 * 2 * 1) = 6

Similarly, the number of ways to draw two green marbles is:

2C2 = 2! / 2!(2 - 2)! = 2! / 2!0! = (2 * 1) / (2 * 1 * 1) = 1

The total number of favorable outcomes is the sum of these two possibilities:

6 + 1 = 7

Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:

P(two marbles of the same color) = Number of favorable outcomes / Total number of possible outcomes = 7 / 15 = 0.4667 (rounded to four decimal places) or 46.67% (rounded to two decimal places).

Therefore, the probability of drawing two marbles with the same color is approximately 0.4667 or 46.67%.

If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.

For blue = 4/6 * 3/5 = 2/5

For green = 2/6 * 1/5 = 1/10

Either-or probabilities are found by adding the individual probabilities.

2/5 + 1/10 = ?

2/5+1/10 is 5/10.

But in my book it states that the answer is 7/15, without an explanation.