A balloon artist counted the number of balloon animal requests he received at a party. The balloon equests differed in animal type and color. Giraffe Dog Purple 8 9 Green 5 6 Yellow 9 3 Vhat is the probability that a randomly selected balloon animal is yellow or is shaped like a giraffe? Simplify any fractions.

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QasimZ611909 QasimZ611909

25-10-2022
Mathematics

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A balloon artist counted the number of balloon animal requests he received at a party. The balloon equests differed in animal type and color. Giraffe Dog Purple 8 9 Green 5 6 Yellow 9 3 Vhat is the probability that a randomly selected balloon animal is yellow or is shaped like a giraffe? Simplify any fractions.

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ErikaV251363 ErikaV251363 · Answer 1 · 2022-10-25T22:26:37+02:00

The probability that a randomly selected balloon animal is yellow or is shaped like a giraffe is given by

[tex]P(yellow\: or\: giraffe)=P(yellow)+P(giraffe)-P(yellow\: and\: giraffe)[/tex]

Let us first find the probability that a randomly selected balloon animal is yellow

[tex]P(yellow)=\frac{n(\text{yellow)}}{n(\text{total)}}[/tex]

Where n(yellow) is the total of the row yellow

[tex]n(yellow)=9+3=12[/tex]

n(total) is the total number of balloon animals

[tex]n(total)=8+9+5+6+9+3=40[/tex]

So, the probability that a randomly selected balloon animal is yellow is

[tex]P(yellow)=\frac{n(\text{yellow)}}{n(\text{total)}}=\frac{12}{40}=\frac{3}{10}[/tex]

Now, let us find the probability that a randomly selected balloon animal is shaped like a giraffe

[tex]P(giraffe)=\frac{n(giraffe\text{)}}{n(\text{total)}}[/tex]

Where n(giraffe) is the total of the column giraffe

[tex]n(giraffe\text{)}=8+5+9=22[/tex]

So, the probability that a randomly selected balloon animal is shaped like a giraffe is

[tex]P(giraffe)=\frac{n(giraffe\text{)}}{n(\text{total)}}=\frac{22}{40}=\frac{11}{20}[/tex]

Now, let us find the probability that a randomly selected balloon animal is yellow and shaped like a giraffe

[tex]P(yellow\: and\: giraffe)=\frac{n(yellow\: and\: giraffe)}{n(\text{total)}}[/tex]

Where n(yellow and giraffe) is 9 (the intersection of yellow and giraffe)

[tex]P(yellow\: and\: giraffe)=\frac{n(yellow\: and\: giraffe)}{n(\text{total)}}=\frac{9}{40}[/tex]

Finally, the probability that a randomly selected balloon animal is yellow or is shaped like a giraffe is

[tex]\begin{gathered} P(yellow\: or\: giraffe)=P(yellow)+P(giraffe)-P(yellow\: and\: giraffe) \\ P(yellow\: or\: giraffe)=\frac{3}{10}+\frac{11}{20}-\frac{9}{40} \\ P(yellow\: or\: giraffe)=\frac{5}{8} \end{gathered}[/tex]

Therefore, the probability that a randomly selected balloon animal is yellow or is shaped like a giraffe is 5/8