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Vadim26 [7]
3 years ago
9

Every​ morning, my neighbor goes out walking. I observe that​ 20% of the time she walks with her​ beagle, 70% of the time she wa

lks with her golden​ retriever, and​ 30% of the time she walks alone. If these events are all​ disjoint, is this an example of a valid probability​ distribution?
Mathematics
1 answer:
Oduvanchick [21]3 years ago
5 0

Answer:

No, This is not a valid Probability Distribution

Step-by-step explanation:

Probability [Neighbour walks with Beagle] = 20%

Probability [Neighbour walks with Golden Retriever] = 70%

Probability [Neighbour walks alone] = 30%

Disjoint Events are the events that have zero probability of occurring together. If all the three above items are disjoint, it means that it can never happen that two of them happen together.

The total (summed) probability of a valid probability distribution, with disjoint sets = 1 . In given case, total probability = 0.2 + 0.7 + 0.3 = 1.2 ; i.e > 1.

So, this probability distribution with stated disjoint events is not a Valid Probability distribution.

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20) \displaystyle [4, 1]

19) \displaystyle [-5, 1]

18) \displaystyle [3, 2]

17) \displaystyle [-2, 1]

16) \displaystyle [7, 6]

15) \displaystyle [-3, 2]

14) \displaystyle [-3, -2]

13) \displaystyle NO\:SOLUTION

12) \displaystyle [-4, -1]

11) \displaystyle [7, -2]

Step-by-step explanation:

20) {−2x - y = −9

{5x - 2y = 18

⅖[5x - 2y = 18]

{−2x - y = −9

{2x - ⅘y = 7⅕ >> New Equation

__________

\displaystyle \frac{-1\frac{4}{5}y}{-1\frac{4}{5}} = \frac{-1\frac{4}{5}}{-1\frac{4}{5}}

\displaystyle y = 1[Plug this back into both equations above to get the x-coordinate of 4]; \displaystyle 4 = x

_______________________________________________

19) {−5x - 8y = 17

{2x - 7y = −17

−⅞[−5x - 8y = 17]

{4⅜x + 7y = −14⅞ >> New Equation

{2x - 7y = −17

_____________

\displaystyle \frac{6\frac{3}{8}x}{6\frac{3}{8}} = \frac{-31\frac{7}{8}}{6\frac{3}{8}}

\displaystyle x = -5[Plug this back into both equations above to get the y-coordinate of 1]; \displaystyle 1 = y

_______________________________________________

18) {−2x + 6y = 6

{−7x + 8y = −5

−¾[−7x + 8y = −5]

{−2x + 6y = 6

{5¼x - 6y = 3¾ >> New Equation

____________

\displaystyle \frac{3\frac{1}{4}x}{3\frac{1}{4}} = \frac{9\frac{3}{4}}{3\frac{1}{4}}

\displaystyle x = 3[Plug this back into both equations above to get the y-coordinate of 2]; \displaystyle 2 = y

_______________________________________________

17) {−3x - 4y = 2

{3x + 3y = −3

__________

\displaystyle \frac{-y}{-1} = \frac{-1}{-1}

\displaystyle y = 1[Plug this back into both equations above to get the x-coordinate of −2]; \displaystyle -2 = x

_______________________________________________

16) {2x + y = 20

{6x - 5y = 12

−⅓[6x - 5y = 12]

{2x + y = 20

{−2x + 1⅔y = −4 >> New Equation

____________

\displaystyle \frac{2\frac{2}{3}y}{2\frac{2}{3}} = \frac{16}{2\frac{2}{3}}

\displaystyle y = 6[Plug this back into both equations above to get the x-coordinate of 7]; \displaystyle 7 = x

_______________________________________________

15) {6x + 6y = −6

{5x + y = −13

−⅚[6x + 6y = −6]

{−5x - 5y = 5 >> New Equation

{5x + y = −13

_________

\displaystyle \frac{-4y}{-4} = \frac{-8}{-4}

\displaystyle y = 2[Plug this back into both equations above to get the x-coordinate of −3]; \displaystyle -3 = x

_______________________________________________

14) {−3x + 3y = 3

{−5x + y = 13

−⅓[−3x + 3y = 3]

{x - y = −1 >> New Equation

{−5x + y = 13

_________

\displaystyle \frac{-4x}{-4} = \frac{12}{-4}

\displaystyle x = -3[Plug this back into both equations above to get the y-coordinate of −2]; \displaystyle -2 = y

_______________________________________________

13) {−3x + 3y = 4

{−x + y = 3

−⅓[−3x + 3y = 4]

{x - y = −1⅓ >> New Equation

{−x + y = 3

________

\displaystyle 1\frac{2}{3} ≠ 0; NO\:SOLUTION

_______________________________________________

12) {−3x - 8y = 20

{−5x + y = 19

⅛[−3x - 8y = 20]

{−⅜x - y = 2½ >> New Equation

{−5x + y = 19

__________

\displaystyle \frac{-5\frac{3}{8}x}{-5\frac{3}{8}} = \frac{21\frac{1}{2}}{-5\frac{3}{8}}

\displaystyle x = -4[Plug this back into both equations above to get the y-coordinate of −1]; \displaystyle -1 = y

_______________________________________________

11) {x + 3y = 1

{−3x - 3y = −15

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\displaystyle \frac{-2x}{-2} = \frac{-14}{-2}

\displaystyle x = 7[Plug this back into both equations above to get the y-coordinate of −2]; \displaystyle -2 = y

I am delighted to assist you anytime my friend!

7 0
3 years ago
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