Answer:
[tex]P(Red\ or\ Blue) = \frac{11}{16}[/tex]
Step-by-step explanation:
Given
[tex]Red = 9[/tex]
[tex]Blue = 2[/tex]
[tex]Yellow = 5[/tex]
Required
Probability of Red or Blue
First, it should be noted that the event described in the question are mutually exclusive or disjoint events;
Meaning that the probability of one have no effect the other;
Having said that; the Probability of Red ot Blue is as follows
[tex]P(Red\ or\ Blue) = P(Red) + P(Blue)[/tex]
Calculating [tex]P(Blue)[/tex]
[tex]P(Blue) = Number\ of\ blue\ crayon / total\ crayon[/tex]
[tex]P(Blue) = \frac{2}{9+ 2 + 5}[/tex]
[tex]P(Blue) = \frac{2}{16}[/tex]
Calculating [tex]P(Red)[/tex]
[tex]P(Red) = Number\ of\ red\ crayon / total\ crayon[/tex]
[tex]P(Red) = \frac{9}{9+ 2 + 5}[/tex]
[tex]P(Red) = \frac{9}{16}[/tex]
Substitute these values in the formula given above
[tex]P(Red\ or\ Blue) = P(Red) + P(Blue)[/tex]
[tex]P(Red\ or\ Blue) = \frac{9}{16} + \frac{2}{16}[/tex]
Take LCM
[tex]P(Red\ or\ Blue) = \frac{9 + 2}{16}[/tex]
[tex]P(Red\ or\ Blue) = \frac{11}{16}[/tex]
Hence, the probability of a red or blue crayon is
[tex]P(Red\ or\ Blue) = \frac{11}{16}[/tex]
