please show me the steps that you use to solve the problem. you can also use the comment field to explain the work.
QUESTION:
1. what is the probability of selecting a red marble, replacing it, and then selecting a blue marble? show work
2. what is the probability of selecting a red marble, setting it aside, and then selecting a blue marble? show your work
3. are the answers to parts (a) and (b) the same? why or why not?
KEY:
4 red marbles
7 blue marbles
5 green marbles
4 red out of a total of 16
4/16 of a red
You replace the red so you still have 16
7/16 chance of a blue
AND means both events have to happen to you multiply the two fractions.
2) there is no replacement.
Getting the same is the same as in #1 But... getting the blue is now 7/15 because we did not replace the marble,
Multiple 4/16 times 7/15
The answers are not the same because in the first question there was replacement and in the second question there was no replacement.
To solve these problems, we need to understand the concept of probability. Probability is a measure of how likely an event is to occur. In these problems, we are dealing with situations where marbles are being selected from a bag with different colors.
Let's solve each question step by step:
Question 1: What is the probability of selecting a red marble, replacing it, and then selecting a blue marble?
Step 1: Find the probability of selecting a red marble.
Given that there are a total of 4 red marbles and the total number of marbles is 4 + 7 + 5 = 16, the probability of selecting a red marble is P(Red) = 4/16 = 1/4.
Step 2: Find the probability of selecting a blue marble.
Since we are replacing the red marble back into the bag, the total number of marbles remains the same. So, the probability of selecting a blue marble is also P(Blue) = 7/16.
Step 3: Find the probability of both events happening.
To find the probability of two independent events happening, we multiply their individual probabilities. So, the probability of selecting a red marble and then a blue marble is P(Red and Blue) = P(Red) * P(Blue).
P(Red and Blue) = (1/4) * (7/16) = 7/64.
Question 2: What is the probability of selecting a red marble, setting it aside, and then selecting a blue marble?
Step 1: Find the probability of selecting a red marble.
As discussed earlier, P(Red) = 1/4.
Step 2: Find the probability of selecting a blue marble.
Since we are setting the red marble aside, the total number of marbles decreases by 1. So, the probability of selecting a blue marble becomes P(Blue) = 7/15.
Step 3: Find the probability of both events happening.
Following a similar approach as in Question 1, P(Red and Blue) = P(Red) * P(Blue).
P(Red and Blue) = (1/4) * (7/15) = 7/60.
Question 3: Are the answers to parts (a) and (b) the same? Why or why not?
No, the answers to parts (a) and (b) are not the same. The reason is that in part (a), we replaced the red marble back into the bag, while in part (b), we set it aside. In part (b), after the red marble is set aside, the total number of marbles decreases, affecting the probability of selecting the blue marble. Therefore, the probabilities are different.