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Umnica [9.8K]
3 years ago
10

A carnival is being set up in your hometown. From experience, the carnival organizer knows that the amount of money he will brin

g in depends on the weather. If it is rainy, he will lose $5,000. If it is cloudy, he expects to earn $4,000. If it is sunny, he will bring in $12,000. The weather forecast shows that there is a 20% chance of rain and a 50% chance of sunny skies. Otherwise, it will be cloudy.A carnival is being set up in your hometown. From experience, the carnival organizer knows that the amount of money he will bring in depends on the weather. If it is rainy, he will lose $5,000. If it is cloudy, he expects to earn $4,000. If it is sunny, he will bring in $12,000. The weather forecast shows that there is a 20% chance of rain and a 50% chance of sunny skies. Otherwise, it will be cloudy.
Mathematics
1 answer:
pentagon [3]3 years ago
8 0

Answer:

$6,200

Step-by-step explanation:

The question is to find the expected value.

We know the expected value of a scenario is the sum of the products of each probability of event and its profit or loss.

There are 3 probabilities in the scenario:

Rainy: 20% = 20/100 = 0.2

Sunny: 50% = 50/100 = 0.5

Cloudy: Rest, which is 100 - (50+20) = 100 - 70 = 30% = 30/100 = 0.3

Now, the gain and loss is:

Rainy: Lose 5000 means -5000

Cloudy: Gain 4000 means +4000

Sunny: Gain 12,000 means +12,000

Now, the expected value is:

Expected Value = (0.2)(-5000) + (0.5)(12000) + (0.3)(4000) =  $6,200

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The sum of two numbers is 14 and sum of their squares is 100.Find the numbers
Misha Larkins [42]

Answer:

8 and 6

Step-by-step explanation:

8*8=64

6*6=36

36+64=100

6 0
2 years ago
A large pool of adults earning their first driver’s license includes 50% low-risk drivers, 30% moderate-risk drivers, and 20% hi
Mamont248 [21]

Answer:

The probability that these four will contain at least two more high-risk drivers than low-risk drivers is 0.0488.

Step-by-step explanation:

Denote the different kinds of drivers as follows:

L = low-risk drivers

M = moderate-risk drivers

H = high-risk drivers

The information provided is:

P (L) = 0.50

P (M) = 0.30

P (H) = 0.20

Now, it given that the insurance company writes four new policies for adults earning their first driver’s license.

The combination of 4 new drivers that satisfy the condition that there are at least two more high-risk drivers than low-risk drivers is:

S = {HHHH, HHHL, HHHM, HHMM}

Compute the probability of the combination {HHHH} as follows:

P (HHHH) = [P (H)]⁴

                = [0.20]⁴

                = 0.0016

Compute the probability of the combination {HHHL} as follows:

P (HHHL) = {4\choose 1} × [P (H)]³ × P (L)

               = 4 × (0.20)³ × 0.50

               = 0.016

Compute the probability of the combination {HHHM} as follows:

P (HHHL) = {4\choose 1} × [P (H)]³ × P (M)

               = 4 × (0.20)³ × 0.30

               = 0.0096

Compute the probability of the combination {HHMM} as follows:

P (HHMM) = {4\choose 2} × [P (H)]² × [P (M)]²

                 = 6 × (0.20)² × (0.30)²

                 = 0.0216

Then the probability that these four will contain at least two more high-risk drivers than low-risk drivers is:

P (at least two more H than L) = P (HHHH) + P (HHHL) + P (HHHM)

                                                            + P (HHMM)

                                                  = 0.0016 + 0.016 + 0.0096 + 0.0216

                                                  = 0.0488

Thus, the probability that these four will contain at least two more high-risk drivers than low-risk drivers is 0.0488.

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3 years ago
Find the volume of a pyramid with a square base, where the perimeter of the base is 10.1\text{ ft}10.1 ft and the height of the
rjkz [21]

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28.5 ft^3

58.3 m^3

Step-by-step explanation:

volume of a pyramid = 1/3 x length x width x height

Perimeter of a pyramid = 4 x length

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length = 10.1 / 4 = 2.525

1/3 x (2.525 x 2.525 x 13.4) = 28.5 ft^3

1/3 x (6.1 x 6.1 x 4.7) = 58.3 m^3

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Answer:

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Step-by-step explanation:

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