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Marina86 [1]
3 years ago
9

6. E1 and E2 are events from the same sample space; P(E1)=0.37, P(E2)=0.45, and P(E1, E2)=0.14. a. Find the probability that E2

does not occur. b. Find the probability that either E1 or E2 occurs. c. Find the probability that neither E1 nor E2 occurs.
Mathematics
1 answer:
puteri [66]3 years ago
5 0

Answer:

a. 0.55

b. 0.68

c. 0.18

Step-by-step explanation:

a. The probability that E2 does not occur is one minus the probability that E2 occurs:

1-P(E2)= 1- 0.45\\1-P(E2) = 0.55

b. The probability that either E1 or E2 occurs is given by the sum of their individual probabilities minus their joint probability:

P(E1\ or\ E2) = P(E1)+P(E2)-P(E1, E2)\\P(E1\ or\ E2)=0.37+0.45-0.14\\P(E1\ or\ E2)=0.68

c. The probability that neither E1 nor E2 occurs is one minus the probability of E1 occurring minus the probability of E2 occurring:

1-P(E1)-P(E2)= 1- 0.37 -0.45\\1-P(E1)-P(E2) = 0.18

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A migrating bird flies 576 miles in 16 hours.How many miles does it fly in 3 hours
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Answer: It flies 108 miles in 3 hours.

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3 years ago
Kelly earns 15% more than her sister, and together they earn $999.75. How much does Kelly earn per week?
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Step-by-step explanation:

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5 0
3 years ago
You’re instructed to prepare for a promotional candle sale you will use to test the popularity of the two redesigned candles. Wi
Anuta_ua [19.1K]

Answer:

THE SMALLEST FORMS:

- smallest prism ---> the cube with all sides 2 ==> the volume is 2*2*2 = 8 cm^3

- smallest pyramid number one ---> the pyramid with base sides 2 and the height also 2 ==> the volume is (1/3)*2*2*2 = 8/3 cm^3

- smallest pyramid number two ---> the pyramid with base sides 2 and the lateral sides also 2 ==> the radius of the base is sqrt(2) ==> [pyramid_height]^2 = [lateral_side]^2 - [base_radius]^2 = 2^2 - sqrt(2)^2 = 4 - 2 = 2 ==> pyramid_height = sqrt(2) ==> the volume is (1/3)*2*2*sqrt(2) = 4*sqrt(2)/3 cm^3

- smallest cylinder --> the cylinder of diameter 2 and height also 2 ==> the radius is diameter/2 = 2/2 = 1 ==> the volume is pi*(radius^2)*height = pi*(1^2)*2 = pi*1*2 = 2*pi cm^3

The lesser volume is the volume of the smallest pyramid number two. ==> it's wax cost is approximately 0.0075 * 4 * 1.42 / 3 $ per candle = 0.014 $ per candle ==> the total cost  per candle is approximately 0.014 + 1.6 = 1.614 $ per candle.

THE BIGGEST FORMS:

- biggest prism ---> the cube with all sides 10 ==> the volume is 10*10*10 = 1000 cm^3

- biggest pyramid number one ---> the pyramid with base sides 10 and the height also 10 ==> the volume is (1/3)*10*10*10 = 1000/3 cm^3

- biggest pyramid number two ---> the pyramid with base sides 10 and the lateral sides also 10 ==> the radius of the base is 5*sqrt(2) ==> [pyramid_height]^2 = [lateral_side]^2 - [base_radius]^2 = 10^2 - [5*sqrt(2)]^2 = 100 - 50 = 50 ==> pyramid_height = 5*sqrt(2) ==> the volume is (1/3)*10*10*5*sqrt(2) = 500*sqrt(2)/3 cm^3

- biggest cylinder --> the cylinder of diameter 10 and height also 10 ==> the radius is diameter/2 = 10/2 = 5 ==> the volume is pi*(radius^2)*height = pi*(5^2)*10 = pi*25*10 = 250*pi cm^3

The bigger volume is the volume of the biggest prism (the side-10 cube). ==> it's wax cost is  0.0075 * 1000 $ per candle = 7.5 $ per candle ==> the total cost per candle is 7.5 + 1.6 = 9.1 $ per candle

The range of the cost is the interval [1.614 ; 9.1]. Depending on other prices on the market,  you greed, and other factors you will put a profit margin: maybe 20% of the cost ; maybe a fixed margin like 5$. So the price per candle will be the cost per candle plus the profit margin per candle.

If I were to choose the base length I would have to say 6 because it is the arithmetic mean between 2 and 10: (2+10)/2 = 12/2 = 6. 2cm is too small, and 10cm is too big.

Also if you start with a rectangle of length 10 and width 2 and you have to find the rectangle with the largest area by being allowed to increase the width and decrease the width with the same quantity you get this:

Area of the new rectangle is (10-x)(2+x) = -x^2 + 8x + 20 = -x^2 + 8x -16 + 36 = -(x^2 - 2*x*4 + 4^2) + 36 = -(x-4)^2 + 36 = 36 - (x-4)^2 which has the maximum value of 36 because out of 36 you subtract a positive value. You get the maximum when (x-4)^2 = 0 ==> x-4=0 ==> x=4

The new length is 10-4=6 and the new width is 2+4=6.

Next I would choose the height of the prism (I like prisms :P) to be [the_golden_ratio]*[base_side] which is approximately 1.618 * 6 = 9.708 which I would round up to 10. ==> The volume would be 6*6*10 = 360 cm^3. ==> the cost would be 0.0075*360 + 1.6 = 2.7 + 1.6 = 4.3 $ per candle. And because my candle is so perfect I'd put the profit margin to be 5.69 $ per candle so I can proudly show it in the store with the price of 4.3 + 5.69 = 9.99 $ :)

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2 years ago
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D. People who shop in bookstores are likely to read more books than those who do not.
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