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A bag of candy contains 4 strawberry flavored gumdrops, and 5 orange flavored gumdrops. If Billy reaches in, takes one out and eats it, and then 20 minutes later selects another and eats that one as well, what is the probability that they were both orange flavored gumdrops?

Respuesta :

Let:

A = Select an orange flavored gumdrop

N = Total number of candies

n = Number of orange flavored gumdrops.

so:

[tex]\begin{gathered} P(A_1)=\frac{n}{N} \\ P(A_1)=\frac{5}{20} \\ P(A_1)=\frac{1}{4} \end{gathered}[/tex]

20 minutes later:

[tex]\begin{gathered} P(A_2)=\frac{n-1}{N-1} \\ P(A_2)=\frac{4}{19} \end{gathered}[/tex]

Since they are independent events:

[tex]\begin{gathered} P(A_1\cap A_2)=\frac{1}{4}\times\frac{4}{19} \\ P(A_1\cap A_2)=\frac{1}{19} \end{gathered}[/tex]