A bag contains 4 white, 3 blue, and 5 red marbles.
1. Find the probability of choosing a red marble, then a white marble if the marbles are replaced
1/12
5/36
5/6
5/12
2. Find the probability of choosing 3 blue marbles in a row if the marbles are replaced.
2/11
1/220
1/27
1/64
3. Find the probability of choosing a blue marble then a red marble if the marbles are not replaced.
5/44
15/35
2/3
1/15
4. Find the probability of choosing 2 white marbles in a row if the marbles are not replaced.
1/11
1/9
2/3
1/16
Please indicate your answer choices, so they can be checked.
To solve these probability questions, we need to understand how to calculate probability and apply that knowledge to the given scenarios.
Probability can be defined as the likelihood or chance of an event occurring. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Let's now solve each of the given questions step by step:
1. Find the probability of choosing a red marble, then a white marble if the marbles are replaced.
If the marbles are replaced, it means that the probability of picking a marble remains the same for each draw.
The total number of marbles in the bag is 4 white + 3 blue + 5 red = 12.
First, we calculate the probability of choosing a red marble. Since there are 5 red marbles out of 12 total marbles, the probability of choosing a red marble is 5/12.
Next, we calculate the probability of choosing a white marble. Since there are 4 white marbles out of 12 total marbles (considering 5 red marbles have already been chosen and replaced), the probability of choosing a white marble is also 4/12.
To find the probability of both events occurring (choosing a red marble then a white marble), we multiply the probabilities together: (5/12) * (4/12) = 20/144 = 5/36.
Therefore, the answer to question 1 is 5/36.
2. Find the probability of choosing 3 blue marbles in a row if the marbles are replaced.
Again, since the marbles are replaced, the probability of picking a marble remains the same for each draw.
The probability of picking a blue marble is 3/12.
Since we are drawing three blue marbles in a row, we multiply the probabilities together: (3/12) * (3/12) * (3/12) = 27/1728 = 1/64.
Therefore, the answer to question 2 is 1/64.
3. Find the probability of choosing a blue marble then a red marble if the marbles are not replaced.
When the marbles are not replaced, the probability changes for each draw since the total number of marbles decreases.
The total number of marbles in the bag is initially 4 white + 3 blue + 5 red = 12.
First, we calculate the probability of choosing a blue marble. Since there are 3 blue marbles out of 12 total marbles, the probability of choosing a blue marble is 3/12.
After picking a blue marble, the total number of marbles becomes 11 (since one marble has been drawn). Out of these 11 marbles, there are still 5 red marbles remaining. Therefore, the probability of choosing a red marble after a blue marble has been drawn is 5/11.
To find the probability of both events occurring (choosing a blue marble then a red marble), we multiply the probabilities together: (3/12) * (5/11) = 15/132 = 5/44.
Therefore, the answer to question 3 is 5/44.
4. Find the probability of choosing 2 white marbles in a row if the marbles are not replaced.
When the marbles are not replaced, the probability changes for each draw since the total number of marbles decreases.
The total number of marbles in the bag is initially 4 white + 3 blue + 5 red = 12.
First, we calculate the probability of choosing a white marble. Since there are 4 white marbles out of 12 total marbles, the probability of choosing a white marble is 4/12.
After picking a white marble, the total number of marbles becomes 11 (since one marble has been drawn). Out of these 11 marbles, there are still 3 white marbles remaining. Therefore, the probability of choosing a white marble after a white marble has been drawn is 3/11.
To find the probability of both events occurring (choosing two white marbles in a row), we multiply the probabilities together: (4/12) * (3/11) = 12/132 = 1/11.
Therefore, the answer to question 4 is 1/11.