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alex41 [277]
3 years ago
13

The weather forecast for the weekend is a 34% chance of rain for Saturday and a 32% chance of rain for Sunday. If we assume that

consecutive days are independent events, What is the probability that it rains over the weekend (either Saturday or Sunday)? Please use 3 decimal places.
Mathematics
1 answer:
kaheart [24]3 years ago
6 0

Answer:

P( A \cap B) = P(A) *P(B) = 0.34*0.32 = 0.1088

And then replacing in the total probability formula we got:

P(A \cup B) = 0.34+0.32 - 0.1088 = 0.5512

And rounded we got P(A \cup B ) = 0.551

That represent the probability that it rains over the weekend (either Saturday or Sunday)

Step-by-step explanation:

We can define the following notaton for the events:

A = It rains over the Saturday

B = It rains over the Sunday

We have the probabilities for these two events given:

P(A) = 0.34 , P(B) = 0.32

And we are interested on the probability  that it rains over the weekend (either Saturday or Sunday), so we want to find this probability:

P(A \cup B)

And for this case we can use the total probability rule given by:

P(A \cup B) = P(A) + P(B) - P(A \cap B)

And since we are assuming the events independent we can find the probability of intersection like this:

P( A \cap B) = P(A) *P(B) = 0.34*0.32 = 0.1088

And then replacing in the total probability formula we got:

P(A \cup B) = 0.34+0.32 - 0.1088 = 0.5512

And rounded we got P(A \cup B ) = 0.551

That represent the probability that it rains over the weekend (either Saturday or Sunday)

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\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\
a^{-{ n}} \implies \cfrac{1}{a^{ n}}
\qquad \qquad
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\left( 2^8\cdot 3^{-5}\cdot 6^0 \right)^{-2}\left( \cfrac{3^{-2}}{2^3} \right)^4\cdot 2^{28}\impliedby \textit{let's do the first group}
\\\\
-------------------------------\\\\


\bf \left( 2^8\cdot \cfrac{1}{3^5}\cdot 1 \right)^{-2}\implies \left( \cfrac{2^8}{3^5} \right)^{-2}\implies \left( \cfrac{3^5}{2^8} \right)^{2}\implies \cfrac{3^{2\cdot 5}}{2^{2\cdot 8}}\implies \boxed{\cfrac{3^{10}}{2^{16}}}\\\\
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\textit{now the second group}\qquad \left( \cfrac{3^{-2}}{2^3} \right)^4\implies \left( \cfrac{\frac{1}{3^2}}{2^3} \right)^4\implies \left( \cfrac{1}{2^3\cdot 3^2} \right)^4

\bf \cfrac{1^4}{2^{4\cdot 3}\cdot 3^{4\cdot 2}}\implies \boxed{\cfrac{1}{2^{12}\cdot 3^8}}\\\\
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\\\\\\
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