- #1
mathmari
Gold Member
MHB
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Hey! ![Smiling face with smiling eyes :blush: 😊](https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f60a.png)
Let one of the four sides of a tetrahedron be red, one blue, one green and the fourth side painted with all three colours. We consider the following events :
A: = The tetrahedron falls on a side with red colour.
B: = The tetrahedron falls on a side with a blue colour.
C: = The tetrahedron falls on a side with a green colour
Give a suitable probability space and give the events A, B and C as subsets of the result set.
(a) Show that two of the events A, B and C are independent.
(b) Are A, B, C independent? Explain. Does it hold that $P(A)=P(B)=P(C)=\frac{2}{4}$ because there is one side for each colour the the 4th side contains also each colour?
The probability space is the set of colours, or not?
:unsure:
![Smiling face with smiling eyes :blush: 😊](https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f60a.png)
Let one of the four sides of a tetrahedron be red, one blue, one green and the fourth side painted with all three colours. We consider the following events :
A: = The tetrahedron falls on a side with red colour.
B: = The tetrahedron falls on a side with a blue colour.
C: = The tetrahedron falls on a side with a green colour
Give a suitable probability space and give the events A, B and C as subsets of the result set.
(a) Show that two of the events A, B and C are independent.
(b) Are A, B, C independent? Explain. Does it hold that $P(A)=P(B)=P(C)=\frac{2}{4}$ because there is one side for each colour the the 4th side contains also each colour?
The probability space is the set of colours, or not?
:unsure: