Suppose a jar contains 5 red marbles and 33 blue marbles. If you reach in the jar and pull out 2 marbles at random, find the probability that both are red.
on the first draw, p(red) = 5/38
Now, for the 2nd draw, what is p(red)? One red marble is now missing.
Thanks I found my answer of 10/703
To find the probability that both marbles are red, we need to find the ratio of the number of favorable outcomes (pulling out 2 red marbles) to the total number of possible outcomes (pulling out any 2 marbles).
Step 1: Find the number of favorable outcomes.
Since there are 5 red marbles in the jar, the number of ways to choose 2 red marbles is given by the combination formula:
nCr = (n!) / (r! * (n - r)!)
In this case, n = 5 (total number of red marbles) and r = 2 (number of marbles to be chosen).
So, the number of favorable outcomes is:
nCr = (5!) / (2! * (5 - 2)!) = (5!)/(2! * 3!) = (5 * 4 * 3 * 2 * 1) / (2 * 1 * 3 * 2 * 1) = 10
Step 2: Find the total number of possible outcomes.
The jar contains a total of 5 red marbles and 33 blue marbles, giving us a total of 38 marbles. The number of ways to choose 2 marbles from a total of 38 is given by the combination formula:
nCr = (n!) / (r! * (n - r)!)
In this case, n = 38 (total number of marbles in the jar) and r = 2 (number of marbles to be chosen).
So, the total number of possible outcomes is:
nCr = (38!) / (2! * (38 - 2)!) = (38!)/((2! * 36!) = (38 * 37 * 36 * 35 * ... * 3 * 2 * 1) / (2 * 1 * 36!)= (38 * 37) / (2 * 1) = 703
Step 3: Calculate the probability.
The probability of both marbles being red is:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Probability = 10 / 703
Hence, the probability that both marbles drawn are red is approximately 0.0142 (rounded to 4 decimal places).
To find the probability of pulling out two red marbles, we need to determine the total number of possible outcomes and the number of favorable outcomes.
First, let's calculate the total number of possible outcomes. If we randomly select 2 marbles from a jar containing a total of 38 marbles (5 red + 33 blue), we can use the concept of combinations. The total number of possible outcomes is given by the number of combinations of selecting 2 marbles out of 38:
C(38, 2) = 38! / (2! * (38 - 2)!) = 703
Now, let's calculate the number of favorable outcomes, which is the number of combinations of selecting 2 red marbles out of 5:
C(5, 2) = 5! / (2! * (5 - 2)!) = 10
Lastly, we can calculate the probability of selecting 2 red marbles by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 10 / 703
≈ 0.0142
Therefore, the probability of pulling out 2 red marbles is approximately 0.0142, or about 1.42%.