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Keith_Richards [23]
2 years ago
11

Arthur is testing the effectiveness of a new acne medication. There are 100 people with acne in the study. Forty patients receiv

ed the acne medication, and 60 other patients did not receive treatment. Fifteen of the patients who received the medication reported clearer skin at the end of the study. Twenty of the patients who did not receive medication reported clearer skin at the end of the study. What is the probability that a patient chosen at random from this study took the medication, given that they reported clearer skin?
A. 15%
B. 33%
C. 38%
D. 43%

Mathematics
2 answers:
jenyasd209 [6]2 years ago
8 0
Here is my answer below.

Reil [10]2 years ago
5 0

Answer:  D. 43 %

Step-by-step explanation:

Let M is the event of receiving medicine,

M' is the event of not receiving medicine,

C is the event of clear skin.

Then According to the question,

Total size of the sample space, n(S) = 100

Number of patient who get the medicine, n(M) = 40

Number of patient who do not get the medicine, n(M') = 60

Number of patient  who received the medication reported clearer skin at the end of the study, n(M\capC) = 15

Therefore, the probability that patient  who received the medication reported clearer skin at the end of the study, P(M\cap C) = \frac{n(M\cap C)}{n(S)} = \frac{15}{100} = 0.15

Number of patient who who did not receive the medication reported clearer skin at the end of the study, n(M\capC) = 20.

Thus, the Number of patient who cleared the skin, n(C) = 15 + 20 = 35

And, the probability that the patient cleared their skin,  P(C) = \frac{n(C)}{n(S)} = \frac{35}{100} = 0.35

Therefore, the probability that a patient chosen at random from this study took the medication, given that they reported clearer skin,

P(\frac{M}{C} ) = \frac{P(M\cap C)}{P(C)}

⇒ P(\frac{M}{C} ) = \frac{0.15}{0.35}

⇒  P(\frac{M}{C} ) = \frac{3}{7}

⇒   P(\frac{M}{C} ) =0.42857142857\approx 0.43

Thus,  P(\frac{M}{C} ) = 0.43 or 43\%

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romanna [79]

<u>We are given</u>

  • Radius of Earth; 6.4 x 100 meters = 640 meters

Clearly, the shape of the earth is a sphere. Thus, to determine the volume of the earth, we will use a formula that determines the volume of a sphere.

\implies \text{Volume of sphere =} \   \dfrac{4\pi r^{3}}{3}

When we substitute the radius in the formula, we get;

\implies\text{Volume of sphere} = \dfrac{4\pi (640)^{3}}{3}

\implies\text{Volume of sphere} = \dfrac{4\pi (640)(640)(640)}{3}

Take π as 3.14

\implies\text{Volume of sphere} = \dfrac{4\pi (640)(640)(640)}{3}

\implies \text{Volume of sphere} = \dfrac{4(3.14)(640)(640)(640)}{3}

Simplify the numerator;

\implies \text{Volume of sphere} = \dfrac{4(3.14)(640)(640)(640)}{3}

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Divide the numerator by 3;

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4 0
1 year ago
uppose that​ Mary's utility function is​ U(W) = W0.5​, where W is wealth. She has an initial wealth of​ $100. How much of a risk
Stels [109]

Note that U(W) = W^{0.5}

Answer:

Mary's risk premium is $0.9375

Step-by-step explanation:

Mary's utility function,  U(W) = W^{0.5}

Mary's initial wealth = $100

The gamble has a 50% probability of  raising her wealth to $115 and a 50% probability of lowering it to $77

Expected wealth of Mary, E_w

E_{w} = (0.5 * $115) + (0.5 * $77)

E_{w} = 57.5 + 38.5

E_{w} = $96

The expected value of Mary's wealth is $96

Calculate the expected utility (EU) of Mary:-

E_u = [0.5 * U(115)] + [0.5 * U(77)]\\E_u = [0.5 * 115^{0.5}] + [0.5 * 77^{0.5}]\\E_u = 5.36 + 4.39\\E_u = \$ 9.75

The expected utility of Mary is $9.75

Mary will be willing to pay an amount P as risk premium to avoid taking the risk, where

U(EW - P) is equal to Mary's expected utility from the risky gamble.

U(EW - P) = EU

U(94 - P) = 9.63

Square root (94 - P) = 9.63

If Mary's risk premium is P, the expected utility will be given by the formula:

E_{u} = U(E_{w} - P)\\E_{u} = U(96 - P)\\E_u = (96 - P)^{0.5}\\(E_u)^2 = 96 - P\\ 9.75^2 = 96 - P\\95.0625 = 96 - P\\P = 96 - 95.0625\\P = 0.9375

Mary's risk premium is $0.9375

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Answer:

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Agata [3.3K]
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Michaela has 11/12 yard of orange fabric and 7/8 yard of green fabric. She uses 1/2 yard of each color for her sewing project. H
Ede4ka [16]

Answer:

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Step-by-step explanation:

The total Michaela started with was ...

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She used a total of 1 yard, so has ...

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Michaela has 19/24 yards (or 28.5 inches) of fabric left over.

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