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A bag contains four red marbles, three yellow marbles, and three purple marbles. You will randomly select one marble from the bag.

Which statements are true regarding the scenario? Check all that apply.

A. The probability you select a red marble is [tex]\frac{2}{5}[/tex].

B. The probability you select a purple marble is [tex]\frac{3}{10}[/tex].

C. [tex]P(\text{Red}) + P(\text{Yellow}) + P(\text{Purple}) = 1[/tex].

D. The probability you select a green marble is 0.

E. The probability you select a yellow marble is [tex]\frac{3}{10}[/tex].

Sagot :

GinnyAnswer
To analyze the scenario of selecting a marble from the bag, let's first summarize the contents of the bag:

- Number of red marbles: 4
- Number of yellow marbles: 3
- Number of purple marbles: 3

Total number of marbles in the bag: [tex]\( 4 + 3 + 3 = 10 \)[/tex]

We will now determine the probability of selecting each type of marble.

1. The probability you select a red marble is [tex]\(\frac{4}{10}\)[/tex]:
The probability can be computed by taking the number of red marbles and dividing it by the total number of marbles:
[tex]\[ P(\text{Red}) = \frac{\text{Number of red marbles}}{\text{Total number of marbles}} = \frac{4}{10} = 0.4 \][/tex]
Therefore, this statement is false because it states the probability as [tex]\(\frac{3}{10}\)[/tex], but the correct probability is [tex]\(\frac{4}{10}\)[/tex], which is 0.4.

2. The probability you select a purple marble is [tex]\(\frac{3}{10}\)[/tex]:
We compute it similarly by dividing the number of purple marbles by the total number of marbles:
[tex]\[ P(\text{Purple}) = \frac{\text{Number of purple marbles}}{\text{Total number of marbles}} = \frac{3}{10} = 0.3 \][/tex]
Therefore, this statement is true.

3. [tex]\( P(\text{Red}) + P(\text{Yellow}) + P(\text{Purple}) = 1 \)[/tex]:
The probabilities of red, yellow, and purple marbles should sum up to 1 as they are the only options available in the bag.
[tex]\[ P(\text{Red}) = 0.4, \quad P(\text{Yellow}) = \frac{3}{10} = 0.3, \quad P(\text{Purple}) = 0.3 \][/tex]
Adding them together:
[tex]\[ P(\text{Red}) + P(\text{Yellow}) + P(\text{Purple}) = 0.4 + 0.3 + 0.3 = 1.0 \][/tex]
Therefore, this statement is true.

4. The probability you select a green marble is 0:
Since there are no green marbles in the bag:
[tex]\[ P(\text{Green}) = \frac{\text{Number of green marbles}}{\text{Total number of marbles}} = \frac{0}{10} = 0 \][/tex]
Therefore, this statement is true.

5. The probability you select a yellow marble is 3:
The correct probability of selecting a yellow marble is:
[tex]\[ P(\text{Yellow}) = \frac{\text{Number of yellow marbles}}{\text{Total number of marbles}} = \frac{3}{10} = 0.3 \][/tex]
Therefore, this statement is false because it incorrectly gives the probability as 3, while the correct value is 0.3.

So, the true statements are:
- The probability you select a purple marble is [tex]\(\frac{3}{10}\)[/tex].
- [tex]\( P(\text{Red}) + P(\text{Yellow}) + P(\text{Purple}) = 1 \)[/tex]
- The probability you select a green marble is 0.
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