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On each of the first three days of January, there is a $\frac{1}{3}$ chance that it will snow where Bob lives. On each of the next four days, there is a $\frac{1}{4}$ chance that it will snow. What is the probability that it snows at least once during the first week of January

Respuesta :

Answer:

The probability would be [tex]\dfrac{7}{12}[/tex].

Step-by-step explanation:

Consider A is the event that there is snowing in first three days and B is the event that there is snowing in next four days.

According to the question,

[tex]P(A)=\frac{1}{3}, \\\\P(B)=\frac{1}{4}[/tex].

Thus, the probability that it snows at least once during the first week of January

= snow in first three days or snow in next four days

[tex]=P(A\cup B)[/tex]

[tex]=P(A)+P(B)-P(A\cap B)[/tex]

[tex]=\frac{1}{3}+\frac{1}{4}-0[/tex]     ( ∵ A and B are independent ⇒ [tex]P(A\cap B)=0[/tex] )

[tex]=\frac{4+3}{12}[/tex]

[tex]=\frac{7}{12}[/tex]

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