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Christine randomly pulls a marble from a bowl. There are 140 marbles in the bowl, of which 80 are black, 28 are green, and the rest are blue.(4 points)
Determine the probability of selecting each of the given colors below. Enter the probability as a simplified fraction, unless it can be written as a whole number.

P(black) =


P(green) =


P(blue) =

P(red) =

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Answer 1

To determine the probabilities of selecting each color of marble, we first need to find out how many blue marbles are in the bowl. We know there are:

- Total marbles = 140
- Black marbles = 80
- Green marbles = 28

The number of blue marbles can be calculated as follows:

\[
\text{Blue marbles} = \text{Total marbles} - (\text{Black marbles} + \text{Green marbles})
\]
\[
\text{Blue marbles} = 140 - (80 + 28) = 140 - 108 = 32
\]

Now we can calculate the probabilities for each color:

1. **P(black)**:
\[
P(\text{black}) = \frac{\text{Number of black marbles}}{\text{Total marbles}} = \frac{80}{140}
\]
To simplify:
\[
P(\text{black}) = \frac{8}{14} = \frac{4}{7}
\]

2. **P(green)**:
\[
P(\text{green}) = \frac{\text{Number of green marbles}}{\text{Total marbles}} = \frac{28}{140}
\]
To simplify:
\[
P(\text{green}) = \frac{2}{10} = \frac{1}{5}
\]

3. **P(blue)**:
\[
P(\text{blue}) = \frac{\text{Number of blue marbles}}{\text{Total marbles}} = \frac{32}{140}
\]
To simplify:
\[
P(\text{blue}) = \frac{16}{70} = \frac{8}{35}
\]

4. **P(red)**:
Since there are no red marbles in the bowl, the probability is:
\[
P(\text{red}) = 0
\]

In conclusion, the probabilities are:

- P(black) = \(\frac{4}{7}\)
- P(green) = \(\frac{1}{5}\)
- P(blue) = \(\frac{8}{35}\)
- P(red) = 0