Suppose a jar contains 8 red marbles and 38 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.
Probab = (8/46)(7/45) = 28/1035
To find the probability that both marbles drawn are red, we need to calculate the probability of selecting one red marble and then, without replacement, selecting another red marble.
Step 1: Total number of marbles in the jar
The jar contains a total of 8 red marbles + 38 blue marbles = 46 marbles.
Step 2: Probability of selecting the first red marble
Since there are 8 red marbles out of a total of 46 marbles, the probability of selecting a red marble as the first draw is 8/46.
Step 3: Probability of selecting the second red marble
After the first red marble is drawn, there are now 7 red marbles remaining out of a total of 45 marbles. So, the probability of selecting a red marble as the second draw, without replacement, is 7/45.
Step 4: Calculate the probability of both marbles being red
The probability of both marbles being red is calculated by multiplying the probabilities from steps 2 and 3: (8/46) * (7/45).
Step 5: Simplify the probability
To simplify the probability, we can multiply the numerator and denominator by 2 to get: (8/46) * (7/45) * (2/2) = (8 * 7) / (46 * 45) = 56 / 2070.
Therefore, the probability that both marbles drawn are red is 56/2070.
To find the probability that both marbles are red, we can use the concept of probability and the formula for calculating the probability of independent events.
First, let's calculate the total number of marbles in the jar: 8 red marbles + 38 blue marbles = 46 marbles in total.
Now, let's determine the number of ways to choose 2 marbles out of the 46. We can use the combination formula, denoted as "nCr," where n is the total number of marbles and r is the number of marbles we want to choose. In this case, it is "46C2."
The formula for nCr is: nCr = n! / (r! * (n - r)!)
Plugging in the values, we get:
46C2 = 46! / (2! * (46 - 2)!)
= 46! / (2! * 44!)
Now, let's calculate the number of ways to choose 2 red marbles out of the 8 available. We can use the same combination formula with n=8 and r=2:
8C2 = 8! / (2! * (8 - 2)!)
= 8! / (2! * 6!)
Now, let's calculate the probability that both marbles drawn are red. We can use the formula:
Probability = Number of favorable outcomes / Total number of possible outcomes
In this case, the number of favorable outcomes is the number of ways to choose 2 red marbles, which is 8C2.
The total number of possible outcomes is the total number of ways to choose 2 marbles, which is 46C2.
Therefore, the probability of drawing 2 red marbles can be calculated as:
Probability = 8C2 / 46C2
Now, let's plug the values into the formula:
Probability = (8! / (2! * 6!)) / (46! / (2! * 44!))
Simplifying and canceling out common terms, we get:
Probability = (8 * 7) / (46 * 45)
= 56 / 2070
= 0.0271 (rounded to four decimal places)
Therefore, the probability that both marbles are red is approximately 0.0271.
8 red and 38 blue
total marbles = 8 + 38 = 46 marbles
8 out of 46 marbles are red, and you want to find out what the probability is that that 2 marbles you pull randomly are both red.
8/46 - red marbles/total marbles
2/46 - 2 red marbles/total marbles
simplify 2/46 to 1/23
1/23 is the final answer