Question

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Part 1
Suppose we​ select, without​ looking, one marble from a bag containing 6 red marbles and 11 green marbles. What is the probability of selecting each of the​ following?
​a) A red marble
​b) A green marble
​c) A purple marble
​d) A red or a green marble
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Part 1
​a) What is the probability of picking a red​ marble?
  
six seventeenths
​(Type an integer or a simplified​ fraction.)
Part 2
​b) What is the probability of picking a green​ marble?
  
StartFraction 11 Over 17 EndFraction
​(Type an integer or a simplified​ fraction.)
Part 3
​c) What is the probability of picking a purple​ marble?
  
enter your response here ​(Type an integer or a simplified​ fraction.)

Answer 1

To find the probabilities for each of the scenarios presented, we first need to determine the total number of marbles in the bag.

**Total marbles = Number of red marbles + Number of green marbles**

Total marbles = 6 (red) + 11 (green) = 17 marbles.

Now we can calculate the probabilities based on the total:

**Part 1:**
**a)** Probability of picking a red marble:
\[
P(\text{red}) = \frac{\text{Number of red marbles}}{\text{Total number of marbles}} = \frac{6}{17}
\]
So, the probability of picking a red marble is \(\frac{6}{17}\).

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**Part 2:**
**b)** Probability of picking a green marble:
\[
P(\text{green}) = \frac{\text{Number of green marbles}}{\text{Total number of marbles}} = \frac{11}{17}
\]
So, the probability of picking a green marble is \(\frac{11}{17}\).

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**Part 3:**
**c)** Probability of picking a purple marble:
Since there are no purple marbles in the bag, the probability is:
\[
P(\text{purple}) = \frac{\text{Number of purple marbles}}{\text{Total number of marbles}} = \frac{0}{17} = 0
\]
So, the probability of picking a purple marble is \(0\).

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