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Hitman42 [59]
3 years ago
15

If 3 marbles are drawn from a bag of 12 marbles consisting of three red, four white and five blue, without returning them to the

bag, what is the probability that the first marble is red the second is white and the third is blue?
Mathematics
1 answer:
FinnZ [79.3K]3 years ago
7 0

Answer:

The probability of that happening is 1/22

Step-by-step explanation:

In order to find the probability, you need to start by finding the probability for each step. The probability of the first one being red is the number of red marbles divided by the total number of marbles.

3 red / 12 total.

3/12

1/4

Now the chance that the second is white is the total number of white marbles divided by how many are left in the bag.

4 white / 11 left

4/11

Lastly, the chance of the last one being blue is the number of blue marbles divided by the amount of total marbles left after two pulls.

5 blue/ 10 left

5/10

1/2

Now to find the overall probability of all 3 happening, we multiply all 3 probabilities together.

1/4 * 4/11 * 1/2 = 1/22

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in 2012, the population of a city was 63,000. by 2017, the population was reduced to approximately 54,100. identify any equation
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Answer:

<em></em>f(x) = 63000(0.97)^x<em></em>

<em></em>

Step-by-step explanation:

Given

f(0) = 63000 ---x = 0, in 2012

f(5) = 54100 -- x = 5, in 2017

Required

Select all possible equations

Because there is a reduction in the population, as time increases; the rate must be less than 1.

An exponential function is represented as:

f(x) = ab^x

Where

b = rate

rate > 1 in options (a) and (b) i.e. 1.03

This implies that (a) and (b) cannot be true

For option (c), we have:

f(x) = 63000(0.97)^x

Set x = 0

f(0) = 63000(0.97)^0 = 63000*1=63000\\

Set x = 5

f(5) = 63000(0.97)^5 = 63000*0.8587=54098.1 \approx 54100

<em>This is true because the calculated values of f(0) and f(5) correspond to the given values</em>

For option (d), we have:

f(x) = 52477(0.97)^x

Set x = 0

f(0) = 52477(0.97)^0 - 52477* 1 = 52477

<em>This is false because the calculated value of f(0) does not correspond to the given value</em>

For option (e), we have:

f(x) = 63000(0.97)^\frac{1}{5x}

Set x = 0

f(0) = 63000(0.97)^\frac{1}{5*0} = 63000(0.97)^\frac{1}{0} =undefined

<em>This is false because the f(x) is not undefined at x = 0</em>

For option (f), we have:

f(x) = 52477(0.97)^{5x

Set x = 0

f(0) = 52477(0.97)^{5*0} = 52477(0.97)^0 =52477*1= 52477

<em>This is false because the calculated value of f(0) does not correspond to the given value</em>

<em>From the computations above, only (c) </em>f(x) = 63000(0.97)^x<em> is true</em>

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