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Katen [24]
3 years ago
11

Each of urns I and II has 5 red balls, 3 white balls, and 2 green balls. Urn III has 1 red ball, 1 white ball, and 8 green balls

. An urn is selected at random and a ball is drawn. If the ball is green, find the probability that urn III was selected. (Enter your probabilities as fractions.)
Mathematics
1 answer:
LekaFEV [45]3 years ago
3 0

Answer:

The probability of selecting the green ball from urn III is ²/₃

Step-by-step explanation:

Given;

total number of balls in urn I = 10

number of green balls in urn I , = 2

total number of balls in urn II = 10

number of green balls in urn II , = 2

total number of balls in urn III = 10

number of green balls in urn II , = 8

P = \frac{\frac{8}{10}  }{\frac{2}{10} + \frac{2}{10}+ \frac{8}{10}}\\\\P =  \frac{\frac{8}{10}  }{\frac{12}{10} }\\\\P = \frac{8}{10}  *\frac{10}{12} \\\\P = \frac{8}{12}\\\\ P = \frac{2}{3}

Therefore, the probability of selecting the green ball from urn III is ²/₃

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During the first part of a​ trip, a canoeist travels 96 miles at a certain speed. the canoeist travels 15 miles on the second pa
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This problem is a problem using 
d = r * t
First part of the trip
d = 96 miles
r = ??
t = ??

Second part of the trip
d = 15 miles
r = r - 5
t = 4 - t

Solve for r first.
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96(r - 5) + 15r  = 4*(r - 5)(r)             Remove the brackets on the left
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111r - 480 = 4r^2 - 20r                     Bring the left side over to the right side.
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The only way I could do this was to use the quadratic equation.

\text{x = }\dfrac{ -b \pm \sqrt{b^{2} - 4ac } }{2a}

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b = - 131

c = 480

\text{x = }\dfrac{ -(-131) \pm \sqrt{(-131)^{2} - 4*4*480 } }{2*4}
\text{x = }\dfrac{ 131 \pm \sqrt{(17161) - 7680 } }{8}
\text{x = }\dfrac{ 131 \pm \sqrt{9481 } }{8}
\text{x = }\dfrac{ 131 \pm 97.37  }{8}

x = (131 + 97.38)/8
x = 28.55
x = (131 - 97.37)/8
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r = 28.55 for the first  part of the trip and
r = 23.55 for the second part of the trip.

Check.
Let's see if the times add up to 4
d/r = t
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15/22.75 = 0.64

The times do = 4, so the rates are correct.

Answers
r1 = 28.55 for the 96 mile trip.
r2 = 23.55 for the 15 mile trip.

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