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Ket [755]
3 years ago
12

You have a bag of 12 blue marbles and 12 red marbles. each are labeled 1-12. so you have 24 marbles in total (1-12 for each colo

r).
you draw one at random, put it back in the bag, and draw the second one.

what is the probability that the first marble is blue and the second marble is a 12?
Mathematics
1 answer:
ohaa [14]3 years ago
4 0

Answer:

Probability that the first marble is blue: 1/2 or 50%

Probably that the second is a 12: 1/12 or 8.3%

Step-by-step explanation:

There's 24 marbles in total with 12 of those being blue. So if you pull out a marble, there's a 12/24 chance of it being blue, which is reduced down to 1/2

Both the red and blue marbles are labeled 1-12, meaning there are two marbles labeled 12. So if you pull out a marble, there's a 2/24 chance that it'll be a 12, which is reduced down to 1/12. Remember that the first marble drawn is put back into the bag, so the second marble's probabilty isn't going to be 2/23

Hope this helps!

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Solve the inequality <br> 3(x – 2) + 1 ≥ x + 2(x + 2)
leva [86]

Answer:

No solution.

Step-by-step explanation:

Step 1: Write inequality

3(x - 2) + 1 ≥ x + 2(x + 2)

Step 2: Solve for <em>x</em>

  1. Distribute: 3x - 6 + 1 ≥ x + 2x + 4
  2. Combine like terms: 3x - 5 ≥ 3x + 4
  3. Add 5 to both sides: 3x ≥ 3x + 9
  4. Subtract 3x on both sides: 0 ≥ 9

Here we see that the statement is false. Therefore, you cannot solve for the inequality.

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3 years ago
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Answer:

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Step-by-step explanation:

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2 years ago
A study of the US clinical population found that 24.1% are diagnosed with a mental disorder, 14.9% are diagnosed with an alcohol
jeka57 [31]

Answer:

a) 0.336

b) 0.207

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

We solve this problem building the Venn's diagram of these probabilities.

I am going to say that:

A is the probability that a person from the clinical population is diagnosed with mental disorder.

B is the probability that a person from the clinical population is diagnosed with alcohol related disorder.

We have that:

A = a + (A \cap B)

In which a is the probability that a person is diagnosed with mental disorder but not alcohol related disorder and A \cap B is the probability that a person is diagnosed with both of these disorders.

By the same logic, we have that:

B = b + (A \cap B)

We find the values of a,b and the intersection, starting from the intersection.

5% are diagnosed with both disorders.

This means that A \cap B = 0.05

14.9% are diagnosed with an alcohol-related disorder

This means that B = 0.149

So

B = b + (A \cap B)

0.149 = b + 0.05

b = 0.099

24.1% are diagnosed with a mental disorder

This means that A = 0.241

So

A = a + (A \cap B)

0.241 = a + 0.05

a = 0.203

(a) What is the probability that someone from the clinical population is diagnosed with a mental disorder, knowing that the person is diagnosed with an alcohol-related disorder?

Desired outcomes:

Mental and alcohol-related disorders, which A \cap B. So D = 0.05

Total outcomes:

Alcohol-related disorder, which is B. So T = 0.149

Probability:

P = \frac{0.05}{0.149} = 0.336

(b) What is the probability that someone from the clinical population is diagnosed with an alcohol-related disorder, knowing that the person is diagnosed with a mental disorder?

Desired outcomes:

Mental and alcohol-related disorders, which A \cap B. So D = 0.05

Total outcomes:

Mental disorder, which is B. So T = 0.241

Probability:

P = \frac{0.05}{0.241} = 0.207

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The answer is C I’m pretty sure
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