You draw two marbles at random from a jar that has 20 red marbles and 30 black marbles without replacement. What is the probability that both marbles are red?
0.1551
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
20/50 * (20-1)/(50-1) = ?
Ah, marbles! They're the colorful little gems of probability. Let's calculate the chances of plucking out two red marbles from the jar.
In the beginning, we have 20 red marbles and 30 black marbles, making a total of 50 marbles.
When you first reach in blindly, you have a 20/50 chance of choosing a red marble. But what happens when you go in a second time?
Well, if you've already snatched a red marble, you're left with 19 red and 30 black marbles out of 49 altogether. So the probability of picking another red marble is 19/49.
Now we put these probabilities together. Since we're looking for the probability of both events happening, we multiply the individual probabilities:
(20/50) * (19/49) = 380/2450
So, the probability that you'll pull out two red marbles is approximately 0.1551, which is about 15.51%.
Remember, though, probabilities are just like marbles... they can roll any way they like!
To find the probability that both marbles are red, we need to calculate the probability of drawing one red marble, and then multiply it by the probability of drawing a second red marble without replacement.
Step 1: Calculate the probability of drawing the first red marble:
The total number of marbles in the jar is 20 red + 30 black = 50 marbles.
The probability of drawing a red marble is 20 red marbles / 50 marbles = 2/5.
Step 2: Calculate the probability of drawing the second red marble (without replacement):
After drawing the first red marble, there will be 19 red marbles left and 49 total marbles. So, the probability of drawing a second red marble is 19 red marbles / 49 marbles = 19/49.
Step 3: Multiply the probabilities from Steps 1 and 2:
The probability of both marbles being red is (2/5) * (19/49) = 0.155 or approximately 15.5%.
Therefore, the probability that both marbles are red when drawing two marbles at random without replacement is 0.155 or approximately 15.5%.
To solve this problem, we need to determine the probability of drawing two red marbles without replacement.
First, let's find the probability of drawing a red marble on the first draw. Since there are 20 red marbles out of a total of 50 (20 red + 30 black), the probability of drawing a red marble on the first draw is 20/50.
Next, for the second draw, we need to consider the reduced number of marbles in the jar. After one red marble has been drawn, there are 49 marbles left in total, with 19 red marbles remaining. Therefore, the probability of drawing a red marble on the second draw, given that the first marble was red, is 19/49.
To find the probability of both marbles being red, we need to multiply the probabilities of each event occurring. So the probability of drawing two red marbles is (20/50) * (19/49), which simplifies to 380/2450.
Finally, we can simplify the probability by dividing both the numerator and denominator by their greatest common divisor, which is 10. So the final probability of drawing two red marbles is 38/245.