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madam [21]
3 years ago
12

Every evening, two weather stations issue weather forecast for the next day. The weather forecasts are independent. On average,

the weather forecast of station 1 is correct 90% of the cases, irrespective of weather type. This percentage is 80% for station 2. Suppose that, without any forecast, the belief is that the next day rains or has sunny weather each with a 50% chance. On a given day, station 1 predicts sunny weather for the next day, whereas station 2 predicts rain. What is the probability that the weather forecast of station 1 will be correct?
Mathematics
1 answer:
EleoNora [17]3 years ago
6 0

Answer:

The probability is 0.6923

Step-by-step explanation:

Let's call R the event that the next day rains, S the event that the next day has sunny weather, R2 the event that the station 2 predicts rain and S1 the event that station 1 predict sunny weather.

The probability that the next day has sunny weather given that station 1 predicts sunny weather for the next day and station 2 predicts rain is calculated as:

P(S/S1∩R2) = P(S∩S1∩R2)/P(S1∩R2)

Where P(S1∩R2) = P(R∩S1∩R2) + P(S∩S1∩R2)

So, the probability P(R∩S1∩R2) that the next day rains, Station 1 predicts sunny weather and Station 2 predicts Rain is calculate as:

P(R∩S1∩R2) = 0.5 * 0.1 * 0.8 = 0.04

Because 0.5 is the probability that the next day rains, 0.1 is the probability that station 1 predicts sunny weather given that it is going to rain and 0.8 is the probability that station 2 predicts rain given that it is going to rain.

At the same way, the probability P(S∩S1∩R2) that the next day has sunny weather, Station 1 predicts sunny weather and Station 2 predicts Rain is calculate as:

P(S∩S1∩R2) = 0.5 * 0.9 * 0.2 = 0.09

Then, the probability P(S1∩R2) that station 1 predicts sunny weather for the next day, whereas station 2 predicts rain is:

P(S1∩R2) = 0.04 + 0.09 = 0.13

Finally, P(S/S1∩R2) is:

P(S/S1∩R2) = 0.09/0.13 = 0.6923

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One number exceeds another number by 6. One fourth of the sum of the two numbers is two less than the smaller.
dolphi86 [110]

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Step-by-step explanation:

let the 2 numbers be x and y , x > y , then

x = y + 6 → (1)

\frac{1}{4} (x + y) = y - 2 ( multiply both sides by 4 to clear the fraction )

x + y = 4y - 8 ( subtract 4y from both sides )

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1 year ago
christy uses glass beads to make braclets and necklances it takes her 30 minutes to make a bracelet and 45 minites to make a nec
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Christy should make at least 30 bracelets and at most 40 necklaces to maximize profit

<h3>How to determine how many bead of each type of bracelets and necklaces should Christy make to maximize his​ profit?</h3>

The given parameters can be represented in the following tabular form:

                       Bracelet (x)    Necklace (y)    Total              

Labor (hour)        0.5                       0.75         40

Profit                    10                         18

From the above table, we have the following:

Objective function:

Max P = 10x + 18y

Subject to:

0.5x + 0.75y <= 40

Because she wants to make at least 30 bracelets, we have:

x >= 30

So, we have:

Max P = 10x + 18y

Subject to:

0.5x + 0.75y <= 40

x >= 30

Express x >= 30 as equation

x = 30

Substitute x = 30 in 0.5x + 0.75y <= 40

0.5 * 30 + 0.75y <= 40

This gives

15 + 0.75y <= 40

Subtract 15 from both sides

0.75y <= 30

Divide by 0.75

y <= 40

Hence, Christy should make at least 30 bracelets and at most 40 necklaces to maximize profit

Read more about maximizing profits at:

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HELPP PLEASE AND GET POINTS
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Answer:

112

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cause if you calculated it it will be 112.2222 so the closest thing is 112

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