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1. A marble will be randomly selected from a bag of solid-colored marbles. The probability of selecting a red marble is [tex]\frac{5}{19}[/tex]. The probability of selecting a blue marble is [tex]\frac{4}{19}[/tex]. What is the probability of selecting a red marble or a blue marble?

A. [tex]\frac{1}{19}[/tex]
B. [tex]\frac{9}{19}[/tex]
C. [tex]\frac{9}{38}[/tex]
D. [tex]\frac{20}{38}[/tex]
E. [tex]\frac{20}{361}[/tex]

The correct answer is [tex]\frac{9}{19}[/tex].


Sagot :

To solve the problem, we need to find the probability of selecting either a red marble or a blue marble from the bag. This can be done by adding the probabilities of selecting a red marble and a blue marble.

Given:
- The probability of selecting a red marble is [tex]\( \frac{5}{19} \)[/tex].
- The probability of selecting a blue marble is [tex]\( \frac{4}{19} \)[/tex].

The probability of selecting a red or a blue marble is the sum of these two probabilities:

[tex]\[ \text{Probability of red or blue} = \frac{5}{19} + \frac{4}{19} \][/tex]

Since the denominators are the same, we can directly add the numerators:

[tex]\[ \text{Probability of red or blue} = \frac{5 + 4}{19} = \frac{9}{19} \][/tex]

Therefore, the probability of selecting a red or blue marble is [tex]\( \frac{9}{19} \)[/tex].

The correct answer is:
B. [tex]\( \frac{9}{19} \)[/tex]