A bag contains 10 red and 8 green marbles. 5 marbles are selected without replacement. What is the probability that exactly 2 are green?
One possible outcome is
GGRRR
the prob of that is (8/18)(7/17)(10/16)(9/15)(8/14)
= 2/51
But the 2 G's and the 3 R's can be arranged in
5!/(2!3!) or 10 ways
so prob of your event = 10(2/51) = 20/51
To find the probability that exactly 2 marbles are green, we need to calculate the probability of selecting 2 green marbles and 3 red marbles from the bag.
Step 1: Determine the total number of ways to select 5 marbles from the bag.
The total number of marbles in the bag is 10 (red) + 8 (green) = 18.
Therefore, the total number of ways to select 5 marbles from 18 marbles is given by the combination formula: C(18,5) = 18! / (5!(18-5)!) = 8568.
Step 2: Determine the number of ways to select exactly 2 green marbles and 3 red marbles.
The number of ways to select exactly 2 green marbles from 8 green marbles is given by the combination formula: C(8,2) = 8! / (2!(8-2)!) = 28.
Similarly, the number of ways to select exactly 3 red marbles from 10 red marbles is given by the combination formula: C(10,3) = 10! / (3!(10-3)!) = 120.
Step 3: Calculate the probability.
The probability of selecting exactly 2 green marbles and 3 red marbles is the ratio of the number of ways to select these marbles to the total number of ways to select 5 marbles.
Therefore, the probability is (28 * 120) / 8568 = 0.39 (rounded to two decimal places).
So, the probability that exactly 2 marbles are green is approximately 0.39.
To find the probability of exactly 2 green marbles being selected, we need to determine the total number of ways to select 5 marbles from the bag, as well as the number of favorable outcomes where exactly 2 marbles are green.
First, let's calculate the total number of ways to select 5 marbles without replacement.
The bag contains a total of 10 + 8 = 18 marbles. Hence, there are 18C5 ways to select 5 marbles from a total of 18 marbles.
Now, let's calculate the number of favorable outcomes, where exactly 2 marbles are green.
We need to choose 2 green marbles from the 8 available green marbles, which can be done in 8C2 ways.
Next, we need to choose the remaining 3 marbles from the 10 red marbles, which can be done in 10C3 ways.
To find the probability, we divide the number of favorable outcomes by the total number of outcomes:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
Therefore, the probability of selecting exactly 2 green marbles is:
Probability = (8C2 * 10C3) / (18C5)
To evaluate the expression further, we can use a calculator or compute the factorial values.