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A marble is selected at random from a jar containing 10 red marbles, 60 yellow marbles, and 30 green marbles. Find the theoretical probability that it is either red or green.
P(red or green)

Must show all work!!



Answer :

Answer:

the probability = [tex]\displaystyle \bf\frac{2}{5}[/tex]

Step-by-step explanation:

We can find the probability of selecting a marble that is either red or green by using the probability formula:

[tex]\boxed{P(A)=\frac{n(A)}{n(S)}}[/tex]

where:

  • [tex]P(A)[/tex] = probability of event A
  • [tex]n(A)[/tex] = total outcomes of event A
  • [tex]n(S)[/tex] = total outcomes of all possibilities

Let:

  • [tex]R[/tex] = selecting a red marble
  • [tex]G[/tex] = selecting a green marble

Then:

  • [tex]n(S)=10+60+30=100[/tex]
  • [tex]n(R)=10[/tex]
  • [tex]n(G) = 30[/tex]

[tex]\displaystyle P(R)=\frac{n(R)}{n(S)}[/tex]

        [tex]\displaystyle=\frac{10}{100}[/tex]

[tex]\displaystyle P(G)=\frac{n(G)}{n(S)}[/tex]

        [tex]\displaystyle=\frac{30}{100}[/tex]

Since event R and event G are independent of each other, therefore:

[tex]\boxed{P(red\ or\ green)=P(R)+P(G)}[/tex]

[tex]\displaystyle P(R\cup G)=\frac{10}{100} +\frac{30}{100}[/tex]

               [tex]\displaystyle=\bf\frac{2}{5}[/tex]

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