A bag contains 5 purple marbles, 7 yellow marbles, and 3 orange marbles. If two marbles are selected from the bag:
What is the probability that an orange then a yellow are chosen with replacement?
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
3/15 * 7/15 = ?
To find the probability of selecting an orange marble followed by a yellow marble with replacement, we need to consider the total number of marbles in the bag and the number of orange and yellow marbles.
First, let's determine the total number of marbles in the bag:
Total Number of Marbles = Number of Purple Marbles + Number of Yellow Marbles + Number of Orange Marbles
= 5 + 7 + 3
= 15
Next, let's calculate the probability of selecting an orange marble. Since there are 3 orange marbles and 15 total marbles, the probability of selecting an orange marble is:
Probability of selecting an Orange Marble = Number of Orange Marbles / Total Number of Marbles
= 3 / 15
= 1/5
Since we are selecting the marbles with replacement, the total number of marbles remains the same even after selecting the first marble.
Therefore, the probability of selecting a yellow marble after selecting an orange marble is also 1/5.
To calculate the probability of both events happening together, we multiply the individual probabilities:
Probability of selecting an orange then a yellow marble = Probability of selecting an Orange Marble * Probability of selecting a Yellow Marble
= 1/5 * 1/5
= 1/25
So, the probability that an orange marble then a yellow marble are chosen with replacement is 1/25 or 0.04 (4%).
To find the probability of events happening one after another, you multiply the individual probabilities of each event.
In this case, when two marbles are selected with replacement, it means that after each selection, the marble is put back into the bag before the next selection.
Let's calculate the probability step-by-step:
1. Probability of selecting an orange marble: There are 3 orange marbles out of a total of 15 marbles in the bag, so the probability of choosing an orange marble on the first draw is 3/15.
2. Probability of selecting a yellow marble: After putting the orange marble back in the bag, we now have 15 marbles in total again, with 7 yellow marbles. So, the probability of selecting a yellow marble on the second draw is 7/15.
3. Multiply the probabilities: To find the probability of both events happening together (an orange followed by a yellow), we multiply the probabilities of each event. Therefore, the probability is (3/15) * (7/15).
Let's calculate the result:
(3/15) * (7/15) = 21/225 = 7/75
So, the probability that an orange marble is chosen followed by a yellow marble (with replacement) is 7/75.