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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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