Two marbles are drawn randomly (without replacement) from a bag containing two green, three yellow, and four red marbles. Find the probability of the event.
Drawing two red marble
step 1 - found it!
STEP 2: Find the number of ways of choosing two marbles.
ways
STEP 3: Find the number of ways of choosing two red marbles.
STEP 4: Find the probability of choosing two red marbles.
following your "steps"
prob(both red) = C(4,2)/C(9,2)
= 6/36
= 1/6
or , straightforward way ....
prob = (4/9)(3/8) = 1/6
Step 1: Finding the number of ways of choosing two marbles.
In this step, we need to find the total number of ways to choose any two marbles from the bag. Since we are drawing without replacement, the number of ways to choose two marbles will be the total number of marbles in the bag choose 2.
In this case, there are 2 green marbles, 3 yellow marbles, and 4 red marbles in total. So the number of ways to choose two marbles is:
(2 + 3 + 4) choose 2 = 9 choose 2 = 36
Step 2: Finding the number of ways of choosing two red marbles.
In this step, we need to find the number of ways to choose two red marbles from the bag. Since we are only interested in choosing red marbles, we need to consider only the 4 red marbles in the bag.
The number of ways to choose two red marbles from the 4 available is:
4 choose 2 = (4!)/(2!(4-2)!) = (4!)/(2!2!) = (4*3)/(2*1) = 6
Step 3: Calculating the probability of choosing two red marbles.
The probability of an event is defined as the number of successful outcomes divided by the total number of possible outcomes. In this case, the successful outcome is choosing two red marbles, and the total number of possible outcomes is choosing any two marbles.
So, the probability of choosing two red marbles is:
Number of ways of choosing two red marbles / Number of ways of choosing two marbles = 6/36 = 1/6
Therefore, the probability of drawing two red marbles from the bag is 1/6.