an urn contains 6 purple marbles and 4 pink marbles. a marble is drawn at random and not replaced. then a second marble is drawn. what is the probability that both marbles are purple?
Ah, probability! Don't worry, I've got just the joke for you:
Why was the math book sad after the probability lesson?
Because it had too many problems!
Now, let's solve your probability problem. We know that there are 6 purple marbles in total, and after one is drawn, there are 9 marbles left, with 5 of them being purple. So the probability of drawing a purple marble on the second attempt, without replacement, is 5/9.
To find the probability of both marbles being purple, we need to multiply the probabilities of the individual events together. So, the probability of drawing two purple marbles without replacement is (6/10) * (5/9).
Calculating that, we get (30/90), which simplifies to 1/3.
So, the probability that both marbles drawn are purple is 1/3. Just like the sad math book from the joke, this problem has a solution!
To find the probability that both marbles drawn from the urn are purple, we need to consider the number of favorable outcomes (both purple marbles) and the total number of possible outcomes.
Given information:
- Number of purple marbles (favorable outcomes): 6
- Total number of marbles (possible outcomes): 6 purple marbles + 4 pink marbles = 10 marbles
We will calculate the probability in two steps:
Step 1: Probability of drawing the first purple marble
Since we draw one marble and do not replace it, the probability of drawing a purple marble on the first draw is 6/10.
Step 2: Probability of drawing the second purple marble
After the first purple marble is drawn, the number of purple marbles decreases to 5, and the total number of marbles decreases to 9 (since one marble has already been drawn).
Therefore, the probability of drawing a second purple marble is 5/9.
Step 3: Multiply the probabilities
To find the probability of both events occurring (drawing two purple marbles), we multiply the probabilities from Step 1 and Step 2:
(6/10) * (5/9) = 30/90 = 1/3
Therefore, the probability that both marbles drawn from the urn are purple is 1/3, or approximately 0.3333.
To find the probability of drawing two purple marbles without replacement, we need to divide the number of favorable outcomes by the number of possible outcomes.
First, let's consider the total number of marbles in the urn: 6 purple marbles + 4 pink marbles = 10 marbles.
To calculate the probability of drawing a purple marble on the first draw, we divide the number of purple marbles (6) by the total number of marbles (10). Therefore, the probability of drawing a purple marble on the first draw is 6/10.
Since the first marble is not replaced, there are now only 9 marbles remaining in the urn (5 purple marbles and 4 pink marbles). To calculate the probability of drawing a purple marble on the second draw, we divide the number of purple marbles (5) by the total number of marbles (9). Therefore, the probability of drawing a purple marble on the second draw is 5/9.
To find the probability of both events occurring, we multiply the probability of the first event (6/10) by the probability of the second event (5/9):
(6/10) * (5/9) = 30/90 = 1/3
Therefore, the probability that both marbles drawn are purple is 1/3 or approximately 0.3333.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
6/10 * 5/9 = ?