(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given [tex]S = \{(r,w)| r,w = 1,2,\ldots, 6\}[/tex]

Deduce the following three probability functions.

Probability that the number of eyes are red

(1)[tex]P_{R}(t) = \frac{1}{6}[/tex] for [tex]t \in \{1,2,\ldots 6 \}[/tex]

Probability that the number of eyes are either red or white

(2)[tex]P_{Y}(t) = \frac{13-2t}{36}[/tex] for [tex]t \in \{1,2,\ldots 6 \}[/tex]

Probability that the number of eyes are either red and white

(3)[tex]P_{Z}(t) = \frac{2t-1}{36}[/tex] for [tex]t \in \{1,2,\ldots 6 \}[/tex]

3. The attempt at a solution

My Proof (1):

Since there is 6 sides on each dice the combined space [tex]S = 6 \cdot 6 = 36 [/tex] and since there is 6 sides on each sides of red dice, then

[tex]\frac{6}{36} = \frac{1}{6} = P_{R}(t)[/tex]

My Proof(2):

The Events of throwing the two dice are describe in the schema:

[tex]

\begin{array}{|c| c| c| c| c| c| }

\hline

(1,1) & (1,2) & (1,3) & (1,4) & (1,5) & (1,6)\\

\hline

(2,1) & (2,2) & (2,3) & (2,4) & (2,5) & (2,6)\\

\hline

(3,1) & (3,2) & (3,3) & (3,4) & (3,5) & (3,6)\\

\hline

(4,1) & (4,2) & (4,3) & (4,4) & (4,5) & (4,6)\\

\hline

(5,1) & (5,2) & (5,3) & (5,4) & (5,5) & (5,6)\\

\hline

(6,1) & (6,2) & (5,3) & (5,4) & (6,5) & (6,6)\\

\hline

\end{array}

[/tex]

Thus by in the schema:

[tex]\begin{array}{ccc} P(x = 1) = \frac{11}{36} & P(x = 2) = \frac{9}{36} & P(x = 3) = \frac{7}{36}\\P(x = 4) = \frac{5}{36} & P(x = 5) = \frac{3}{36} & P(x = 6) = \frac{1}{36} \end{array}[/tex]

which can be describe by the function:

[tex]P_{Y}(t) = \frac{13-2t}{36}[/tex] for [tex]t \in \{1,2,\ldots 6 \}[/tex]

Proof(3)

Thus by in the schema:

[tex]\begin{array}{ccc} P(x = 1) = \frac{1}{36} & P(x = 2) = \frac{3}{36} & P(x = 3) = \frac{5}{36}\\P(x = 4) = \frac{7}{36} & P(x = 5) = \frac{9}{36} & P(x = 6) = \frac{11}{36} \end{array}[/tex]

which can be describe by the function:

[tex]P_{Y}(t) = \frac{2t-1}{36}[/tex] for [tex]t \in \{1,2,\ldots 6 \}[/tex]

What You Guys say I have deduced the probability functions correctly?? Am I on the right track??

SIncerely Yours

Beowulf

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# Homework Help: Throwing Dice

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