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2 years ago

Explain how you are able to get the answer without having to multiply 1.23 by 10 thirteen times.

Mathematics

1 answer:

max2010maxim [7]2 years ago

5 0

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On any given day, the probability that a large local river is polluted by carbon tetrachloride is 0.12. Each day, a test is cond

babymother [125]

Answer:

a) 0.2416

b) 0.4172

c) 0.0253

Step-by-step explanation:

Since the result of the test should be independent of the time , then the that the test number of times that test proves correct is independent of the days the river is correct .

denoting event a A=the test proves correct and B=the river is polluted

a) the test indicates pollution when

- the river is polluted and the test is correct

- the river is not polluted and the test fails

then

P(test indicates pollution)= P(A)*P(B)+ (1-P(A))*(1-P(B)) = 0.12*0.84+0.88*0.16 = 0.2416

b) according to Bayes

P(A∩B)= P(A/B)*P(B) → P(A/B)=P(A∩B)/P(B)

then

P(pollution exists/test indicates pollution)=P(A∩B)/P(B) = 0.84*0.12 / 0.2416 = 0.4172

c) since

P(test indicates no pollution)= P(A)*(1-P(B))+ (1-P(A))*P(B) = 0.84*0.88+ 0.16*0.12 = 0.7584

the rate of false positives is

P(river is polluted/test indicates no pollution) = 0.12*0.16 / 0.7584 = 0.0253

4 0

2 years ago

Two fair number cubes are rolled. What is the probability the numbers are equal or the sum is odd?

Marat540 [252]

Answer:

0.6667 = 66.67%

Step-by-step explanation:

If each number cube has 6 numbers, the two cubes have a total of 6 * 6 = 36 results.

To have equal numbers in each cube, the cases are:

(1,1), (2,2), (3,3), (4,4), (5,5), (6,6) -> 6 cases

To have a odd sum, the cases are:

(1,2), (1,4), (1,6),

(2,1), (2,3), (2,5),

(3,2), (3,4), (3,6),

(4,1), (4,3), (4,5),

(5,2), (5,4), (5,6),

(6,1), (6,3), (6,5). -> 18 cases

So we have a total of 18 + 6 = 24 cases, then the probability is:

P = 24 / 36 = 0.6667 = 66.67%

5 0

2 years ago

The volume of this prism is 4375cm3.<br> The area of the cross-section is 125cm2.<br> Work out x

fomenos

Answer:

x is 35 cm

Step-by-step explanation:

To find the value of x, we will divide the volume by the cross-section

Mathematically, that will be;

4375/125 = 35 cm

5 0

2 years ago

2. Which of the following is frue about the solution to the system of equations below? 2x + 4y = 9 2x + 4y = -9 A. The system ha

Lubov Fominskaja [6]

Answer:

Step-by-step explanation:

B. The system has infinitely many solutions. The system has one solution.

3 0

1 year ago

In a recent survey of 1,700 Game Stop customers 884 of them responed that they play video games on their

kodGreya [7K]

Answer:

52% play video games on their personal computer.

Step-by-step explanation:

884/1700 = 52%

6 0

3 years ago

Explain how you are able to get the answer without having to multiply 1.23 by 10 thirteen times.​

Explain how you are able to get the answer without having to multiply 1.23 by 10 thirteen times.