Suppose a jar contains 6 red marbles and 24 blue marbles. If you reach in the jar and pull out 2 marbles at random, find the probability that both are red
1st marble ... 6 red out of 30 ... 1/5
2nd marble ... 5 red out of 29 ... 5/29
both red ... 1/5 * 5/29
To find the probability of pulling out 2 red marbles, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Step 1: Find the total number of possible outcomes.
In the jar, there are a total of 6 red marbles + 24 blue marbles = 30 marbles.
Step 2: Find the number of favorable outcomes.
To pull out 2 red marbles, we need to choose 2 out of the 6 red marbles. This can be done using the combination formula:
C(n, r) = n! / (r!(n-r)!)
Using this formula, we can calculate:
C(6, 2) = 6! / (2!(6-2)!) = 6! / (2!4!) = (6 * 5 * 4!) / (2! * 4!) = (6 * 5) / 2 = 15
So, there are 15 ways to choose 2 red marbles out of 6.
Step 3: Calculate the probability.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability of pulling out 2 red marbles = Number of favorable outcomes / Total number of possible outcomes = 15 / 30 = 1/2
Therefore, the probability of pulling out 2 red marbles is 1/2 or 0.5.
To find the probability that both marbles drawn are red, we need to divide the number of successful outcomes (when both marbles are red) by the total number of possible outcomes.
First, let's determine the total number of marbles in the jar: 6 red marbles + 24 blue marbles = 30 marbles.
To find the probability of drawing a red marble on the first draw, we take the number of red marbles (6) divided by the total number of marbles (30). So the probability of drawing a red marble on the first draw is 6/30.
After the first marble is drawn, there are now 5 red marbles and 29 marbles left in the jar. To find the probability of drawing a red marble on the second draw, we take the number of red marbles (5) divided by the total number of marbles left (29). So the probability of drawing a red marble on the second draw, given that the first marble was red, is 5/29.
To find the probability that both marbles are red, we need to multiply the probabilities together, as both events need to occur. Therefore, the probability of drawing two red marbles is (6/30) * (5/29) = 1/29, which simplifies to approximately 0.0345.
So the probability that both marbles drawn are red is 1/29, or approximately 0.0345.