a bag contains 3 green marbles, 2 yellow marbles, and 5 blue marbles. a marble is picked at random and replaced. a second marble is picked at random. what is the probability that the first marble is yellow and the second is not yellow.
It is replaced so the drawings are independent
10 marbles total
probability yellow = 2/10
probability not yellow = 8/10
product = 2/10 * 8/10
= 1/5 * 4/5
= 4/25
= 0.16
To find the probability that the first marble is yellow and the second marble is not yellow, we need to determine the probabilities of each event separately and then multiply them together.
Let's calculate the probability of the first marble being yellow:
Total number of marbles = 3 green + 2 yellow + 5 blue = 10 marbles
Number of yellow marbles = 2 yellow marbles
Therefore, the probability of the first marble being yellow = Number of yellow marbles / Total number of marbles = 2 / 10 = 1/5.
Now, since the first marble is picked at random and replaced, the total number of marbles remains the same. Thus, there are still 10 marbles in the bag.
Next, we need to calculate the probability of the second marble not being yellow. Since the first marble is replaced, the total number of marbles doesn't change, but the number of yellow marbles does change.
After the first yellow marble is replaced, the number of yellow marbles is still 2. However, the total number of marbles is now 10 - 1 = 9, as we have removed one yellow marble.
Therefore, the probability of the second marble not being yellow = Number of marbles that are not yellow / Total number of marbles = (9 - 2) / 9 = 7/9.
To find the probability of both events happening together, we multiply the probability of the first marble being yellow (1/5) and the probability of the second marble not being yellow (7/9).
Thus, the probability that the first marble is yellow and the second marble is not yellow = (1/5) * (7/9) = 7/45.
Therefore, the probability is 7/45.