You randomly choose one of the marbles. Without replacing the first marble, you choose a second marble out of 4 marbles
ok - now what?
To solve this problem, we need to calculate the probability of choosing a specific sequence of two marbles out of a set of five marbles, without replacing the first marble.
Let's break it down step by step:
Step 1: Determine the total number of possibilities in choosing the first marble.
In this case, since you randomly choose one marble out of a set of five marbles, the total number of possibilities is 5.
Step 2: Determine the number of possibilities in choosing the second marble.
Since the first marble is not replaced, there will be one fewer marble to choose from in the second draw. Therefore, the number of possibilities in choosing the second marble is 4.
Step 3: Calculate the total number of outcomes.
The total number of outcomes is the product of the number of possibilities in Step 1 and the number of possibilities in Step 2. So, the total number of outcomes is 5 * 4 = 20.
Step 4: Determine the desired outcome.
In this case, the desired outcome is choosing a specific sequence of two marbles out of five. Let's say we're interested in choosing a red marble first, followed by a blue marble.
Step 5: Determine the number of favorable outcomes.
We need to count the number of ways we can get a specific sequence of two marbles out of five. In this case, we want to select a red marble first and a blue marble second. Since there is only one red marble and one blue marble, there is only one favorable outcome.
Step 6: Calculate the probability.
The probability is given by the number of favorable outcomes divided by the total number of outcomes. In this case, the probability is 1/20 = 0.05, or 5%.
So, the probability of randomly choosing a specific sequence of a red marble followed by a blue marble, without replacing the first marble, out of a set of five marbles is 5%.