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Monica [59]
3 years ago
14

For a certain​ candy, 20​% of the pieces are​ yellow, 15​% are​ red, 20​% are​ blue, 20​% are​ green, and the rest are brown. ​a

) If you pick a piece at​ random, what is the probability that it is​ brown? it is yellow or​ blue? it is not​ green? it is​ striped? ​b) Assume you have an infinite supply of these candy pieces from which to draw. If you pick three pieces in a​ row, what is the probability that they are all​ brown? the third one is the first one that is​ red? none are​ yellow? at least one is​ green?
Mathematics
1 answer:
OLEGan [10]3 years ago
4 0

Answer:

Step-by-step explanation:

Based on the question we are given the percentages of each of the types of candies in the bag except for brown. Since the sum of all the percentages equals 75% and brown is the remaining percent then we can calculate that brown is (100-75 = 25%) 25% of the bag. Now we can show the probabilities of getting a certain type of candy by placing the percentages over the total percentage (100%).

  • Brown: \frac{25}{100}
  • Yellow or Blue: \frac{20}{100} +\frac{20}{100} = \frac{40}{100}  ....add the numerators
  • Not Green:  \frac{80}{100}.... since the sum of all the rest is 80%
  • Stiped:  \frac{25}{100} .... there are 0 striped candies.

Assuming the <u><em>ratios/percentages</em></u> of the candies stay the same having an infinite amount of candy will not affect the probabilities. That being said in order to calculate consecutive probability of getting 3 of a certain type in a row we have to multiply the probabilities together. This is calculated by multiplying the numerators with numerators and denominators with denominators.

  • 3 Browns: \frac{25*25*25}{100*100*100} = \frac{15,625}{1,000,000} = \frac{1.5625}{100}

  • the 1st and 3rd are red while the middle is any. We multiply 15% * (total of all minus red which is 85%) * 15% like so.

\frac{15*85*15}{100*100*100} = \frac{19,125}{1,000,000} = \frac{1.9125}{100}

  • None are Yellow: multiply the percent of all minus yellow three times.

\frac{80*80*80}{100*100*100} = \frac{512,000}{1,000,000} = \frac{51.2}{100}

  • At least 1 green: multiply the percent of green by 100% twice, since the other two can by any

\frac{20*100*100}{100*100*100} = \frac{200,000}{1,000,000} = \frac{20}{100}

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Answer:


Step-by-step explanation:

Problem One (left panel)

<em><u>Question A</u></em>

  • The y intercept happens when x = 0
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<em><u>Question B</u></em>

The rate of change = (56 - 52)/(3 - 1) = 4/2 = 2  miles / hour^2 (you have a slight acceleration.

<em><u>Question C</u></em>

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The way I have done it the domain is n from 1 to 6

Question 2 (Right Panel)

<em><u>Question A</u></em>

The equation for the table is f(x) = 3x - 3 which was derived simply by putting all three points into y = ax + b and solving.

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

An open box with a square base is to have a volume of 500 cubic inches.

Let side of the base be x and height of the box is y

Volume of box = area of base × height

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Therefore, y=\dfrac{500}{x^2}

It is open box. The surface area of box, S .

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For maximum/minimum to differentiate S(x)

S'(x)=2x-\dfrac{2000}{x^2}

For critical point, S'(x)=0

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Put x = 10 into y=\dfrac{500}{x^2}

y = 5

Double derivative of S(x)

S''(x)=2+\dfrac{4000}{x^3} at x = 10

S''(10) > 0

Therefore, Surface is minimum at x = 10 inches

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