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At a Phonesmart store, each phone sold is twice as likely to be an Apricot as a Banana. Also each phone sale is independent of any other phone sale. If you monitor the sale of two phones, what is the probability that the two phones sold are the same?

Respuesta :

Answer: The probability that the two phones sold are the same is [tex]\dfrac{5}{9}[/tex]

Step-by-step explanation:

Since we have given that

Let A be the event for Apricot.

Let B be the event for Banana.

And

[tex]P(A)=2P(B)[/tex]

Since phone is either A or B

so, it becomes,

[tex]P(A)+P(B)=1\\\\P(B)+2P(B)=1\\\\3P(B)=1\\\\P(B)=\dfrac{1}{3}[/tex]

So, P(A) is given by

[tex]\dfrac{2}{3}[/tex]

Since two phones are same

So, it becomes,

[tex]P(AA)+P(BB)\\\\=\dfrac{2}{3}\times \dfrac{2}{3}+\dfrac{1}{3}\times \dfrac{1}{3}\\\\=\dfrac{4}{9}+\dfrac{1}{9}\\\\=\dfrac{5}{9}[/tex]

Hence, the probability that the two phones sold are the same is [tex]\dfrac{5}{9}[/tex]

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