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Juliette [100K]
3 years ago
11

A box has eight balls. There are five green balls and three yellow. The five green balls are numbered 1 ,2,3,4 ,and 5. The three

yellow balls are numbered 1,2 ,and 3. The box is shaken.
Answer the following questions, using fractions in p/q format or decimal values accurate to the nearest 0.01 . Here G will mean that a green ball is selected, Y that a yellow ball is selected, and E that an even- numbered ball is selected.

a)a (25%) Select the color/number pairs which comprise the sample

Gl G2 G3 G4 G5 G6 G7 G8 Yl Y2 Y3 Y4 Y5 Y6 (15%)

b)P(G) = C. (15%)

c)P (GE)= d (1596)

d)P(Gr E)= e (1596)

e)P(G U E) = f. (1596) Are G and E mutually exclusive? (pick one)
Mathematics
1 answer:
Soloha48 [4]3 years ago
8 0

Answer:

a) G1, G2, G3, G4, G5, Y1, Y2, Y3

b) P(G) = 5/8

c) P(G|E) = 2/3

d) P(G∩E) = 1/4

e) P(G∪E) = 3/4

G and E are not mutually exclusive

Step-by-step explanation:

Data:

Green Balls = 5 (Numbered 1,2,3,4,5)

Yellow Balls= 3 (Numbered 1,2,3,)

Total Number of Balls = 8

a) The sample space comprises of 5 Green (G) balls numbered 1,2,3,4,5 and 3 Yellow (Y) balls numbered 1,2,3.

So the sample space comprises of:

G1, G2, G3, G4, G5, Y1, Y2, Y3

b) The probability that a green ball is selected can be computed by:

P(G) = Number of Green Balls / Total Number of Balls

P(G) = 5/8

c) <u>P(G|E) = P(G∩E)/P(E)</u>

To calculate P(G∩E), we need to count the number of balls which are green AND even numbered. These are: G2 and G4. The total number of green balls are 8.

So, P(G∩E) = Number of  green and even balls / Total Number of Balls

      <u>P(G∩E) = 2/8 </u>

To calculate P(E), we know that the number of even balls are 3.

P(E) = Number of even balls/Total number of balls

<u>P(E) = 3/8</u>

Therefore,

P(G|E) = (2/8) / (3/8)

P(G|E) = 2/3

d) From the previous part, P(G∩E) = 2/8

It can also be calculated using the conditional probability formula:

P(G|E) = P(G∩E) / P(E)

P(G∩E) = P(E) x P(G|E)

            = (3/8) x (2/3)

P(G∩E) = 2/8 = 1/4

e)P(G∪E) = P(G) + P(E) - P(G∩E)

               = (5/8) + (3/8) - (2/8)

  P(G∪E) = 6/8 = 3/4

For mutually exclusive events, P(AUB) = P(A) + P(B)

Here, P(GUE) = 6/8 , P(G) = 5/8 and P(E) = 3/8

P(GUE) = P(G) + P(E)

6/8 = 5/8 + 3/8

6/8 ≠ 8/8

So, events G and E are NOT Mutually Exclusive

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Hi there!

<u><em>FACTS</em></u><em> :</em>

<em>To see if multiple ratios are proportional, you can write them as fractions, reduce them, and compare them. If the reduced fractions are all the same, then you have proportionnal ratios. You can also write them as fractions and divide the numerator (top number) by its denominator (bottom number), and compare the decimal numbers the same way you would compare the fractions (I personnaly find this method easier because you don't need to simplify the fractions).</em>

<u>STEPS TO ANSWER:</u>

x = 1 ; y = 90 → \frac{1}{90} = 1 ÷ 90 = <u>0.01111111...</u>


x = 2 ; y = 150 → \frac{2}{150} = 2 ÷ 150 = <u>0.0133333...</u>


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x = 4 ; y = 270 → \frac{4}{270} = 4 ÷ 270 = <u>0.0148148...</u>


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<em>** You didn't really need to calculate them all because even the first two decimal numbers weren't equivalent, but I wanted to show you the whole process so I calculated them all.</em>


⇒ If you compare all the decimals you got, you can easily see that they are not the same, which means that the ratios between the values of "x" and the values of "y" are not proportional. Therefore, George's reasoning wasn't good.


There you go! I really hope this helped, if there's anything just let me know! :)

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