A bag has 3 red marbles, 2 purple marbles, and 5 orange marbles. Jamal picks two marbles at random.
What is the Probability of him choosing (orange, then purple) without replacing the first marble he picked?
P.S: I know the answer is 1/9, but I don't know how to do the work
10 marbles in all, so
P(orange, purple) = 5/10 * 2/9 = 1/9
To calculate the probability of Jamal picking an orange marble first and then a purple marble without replacing the first marble he picked, we need to consider the total number of marbles and the number of favorable outcomes.
1. Total number of marbles: There are a total of 3 red marbles + 2 purple marbles + 5 orange marbles = 10 marbles in the bag.
2. First marble choice: Jamal has a 5/10 chance of picking an orange marble (since there are 5 orange marbles out of 10 total marbles).
3. Second marble choice: After Jamal picks an orange marble, there are now 9 marbles left in the bag, including 2 purple marbles. Therefore, Jamal has a 2/9 chance of picking a purple marble (since there are 2 purple marbles out of the remaining 9 marbles).
4. Multiply the probabilities: To find the probability of both events occurring, we multiply the probabilities of each individual event. Therefore, the probability of Jamal choosing an orange marble first and then a purple marble without replacement is (5/10) * (2/9) = 10/90 = 1/9.
So, the probability of Jamal choosing an orange marble first and then a purple marble without replacing the first marble he picked is 1/9.
To find the probability of Jamal choosing an orange marble first and then a purple marble without replacing the first marble, we need to calculate the probability of those two events occurring separately and then multiply them together.
Step 1: Calculate the probability of choosing an orange marble first.
Since there are 5 orange marbles in the bag and a total of 10 marbles, the probability of picking an orange marble first is 5/10 or 1/2.
Step 2: Calculate the probability of choosing a purple marble second, without replacement.
After Jamal picks an orange marble, there are 9 marbles left in the bag, with 2 of them being purple marbles. Therefore, the probability of picking a purple marble second, without replacing the first marble, is 2/9.
Step 3: Multiply the two probabilities together.
To find the overall probability, we multiply the probability of picking an orange marble first (1/2) by the probability of picking a purple marble second (2/9):
(1/2) * (2/9) = 2/18 = 1/9
Therefore, the probability of Jamal choosing an orange marble first and then a purple marble without replacing the first marble is 1/9.