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The Venn Diagram represents a group of children who swam (left circle) and built sandcastles (right circle) at the beach.

Match the symbol or description on the left with its corresponding value on the right. S stands for the event “Swam” and C stands for the event “built sandcastles.” Assume the numbers represent the entire universe.

1. P(S)
1.00
2. P(S or C, but not both)
0.84
3. P(C)
0.16
4. P(S ∪ C)
0.60
5. P(C, but not S)
0.76
6. P(S ∩ C)
0.40

Question

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Respuesta :

evgeniylevi evgeniylevi · Answer 1 · 2019-06-07T13:56:08+02:00

Try this option:

1] P(S)=0.84;

2] P(S or C, but not both)=0.4;

3] P(C)=0.76;

4] P(S∪C)=0.6;

5] P(C, but not S)=0.16;

6] P(S∩C)=1.00.

Answer Link

aquialaska aquialaska · Answer 2 · 2019-07-03T09:19:41+02:00

Answer:

We are given with a Venn diagram.

In Venn Diagram,

S represent Swam

C represent Built Sandcastles.

n( S - (S∩C) ) = 6

n( C - (S∩C) ) = 4

n( S ∩ C ) = 15

To find: P(S) , P(C) , P(S or C, but not Both) = P((S∪C) - (S∩C)) , P( S ∪ C ) ,

P(S ∩ C) , P(C , but not S ) = P(C - (S∩C))

n(S) = n( S - (S∩C) ) + n(S∩C) = 6 + 15 = 21

n(C) = n( C - (S∩C) ) + n(S∩C) = 4 + 15 = 19

n(S∪C) = n( C - (S∩C) ) + n( S - (S∩C) ) + n(S∩C) = 6 + 4 + 15 = 25

Now, [tex]P(S)=\frac{21}{25}=0.84[/tex]

[tex]P(S\:or\:C,\:but\:not\:Both)=P((S\cup C)-(S\cap C))=\frac{10}{25}=0.40[/tex]

[tex]P(C)=\frac{19}{25}=0.76[/tex]

[tex]P(S\cup C)=\frac{25}{25}=1.00[/tex]

[tex]P(C\:,\:but\:not\:S)=P(C - (S\cap C))=\frac{4}{25}=0.16[/tex]

[tex]P(S\cap C)=\frac{15}{25}=0.60[/tex]

Therefore, Match the answers as above.