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 February 9th, 2014, 10:38 AM #1 Newbie   Joined: Oct 2013 Posts: 8 Thanks: 0 Probability of 2 dice and grid/table? Information: Two dice: one of the die has 6 values (numbers one to six) and has six faces, the other die has 4 values (the numbers are 1,1,2,3,6,6) and also six faces. Question: Rolls both dice at the same time... what is the probability of a even number on the first dice and an odd number on the second dice? Answer: P = 3/6 + 3/6 = 6/12? Question: Rolls both dice at the same time... what is the probability of a number 3 on one dice and a number one on the other? Answer: the first dice number 3. P = 1/6? Answer: the second dice number one. P = 2/6? = 3/12??? Question: Draw a 2-way table to illustrate all possible totals then both dice are thrown? I know how to draw a 'fair' 2 dice table (link below) but don't know how to draw a table with one dice showing different values? 2 fair dice table. http://01.edu-cdn.com/files/static/mcgr ... ITY_04.GIF
February 9th, 2014, 01:23 PM   #2
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Re: Probability of 2 dice and grid/table?

Quote:
 Originally Posted by jacob1988 Information: Two dice: one of the die has 6 values (numbers one to six) and has six faces, the other die has 4 values (the numbers are 1,1,2,3,6,6) and also six faces. Question: Rolls both dice at the same time... what is the probability of a even number on the first dice and an odd number on the second dice? Answer: P = 3/6 + 3/6 = 6/12? Question: Rolls both dice at the same time... what is the probability of a number 3 on one dice and a number one on the other? Answer: the first dice number 3. P = 1/6? Answer: the second dice number one. P = 2/6? = 3/12??? Question: Draw a 2-way table to illustrate all possible totals then both dice are thrown? I know how to draw a 'fair' 2 dice table (link below) but don't know how to draw a table with one dice showing different values? 2 fair dice table. http://01.edu-cdn.com/files/static/mcgr ... ITY_04.GIF
You need to learn some elementary probability theory. For starters: if you have two independent events (A and B) with probabilities P(A) and P(B), then the probability of both happening is P(A)xP(B).

For your first question: A = {even number on first die} P(A) = 1/2, B = {odd number on second die} P(B) = 1/2. Since A and B are independent, the probability of both happening = 1/4.

Similarly - second question: prob. (both) = (1/6)x(1/3) = 1/18.

For the table, you simply have a 4 x 6 table. {1,2,3,6} x {1,2,3,4,5,6}

February 9th, 2014, 03:30 PM   #3
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Re: Probability of 2 dice and grid/table?

Hello, jacob1988!

Quote:
 Two dice: one of the dice has 6 faces and numbers {1, 2, 3, 4, 5, 6}. zyhe other die has 6 faces and numbers {1, 1, 2, 3, 6, 6). Question: Both dice are rolled. What is the probability of a even number on the first dice and an odd number on the second dice? Answer: P = 3/6 + 3/6 = 6/12 ?[color=beige] . [/color][color=blue]What?[/color]

$P(\text{even die-1}) \:=\:\frac{3}{6}\,=\,\frac{1}{2}
P(\text{odd die-2}) \,=\,\frac{3}{6} \,=\,\frac{1}{2}$

$P(\text{even die-1 }\wedge\text{ odd die-2}) \:=\:\frac{1}{2}\,\cdot\,\frac{1}{2} \:=\:\frac{1}{4}$

Quote:
 Both dice are rolled. What is the probability of a number 3 on one dice and a number one on the other?

There are two cases to consider.

$\text{(1) 3 on die-1 and 1 on die-2.}
\;\;\;P(\text{3 die-1}) \,=\,\frac{1}{6}
\;\;\;P(\text{1 die-2}) \,=\,\frac{2}{6}\,=\,\frac{1}{3}
P(\text{3 die-1 }\wedge \text{1 die-2}) \:=\:\frac{1}{6}\,\cdot\,\frac{1}{3} \:=\:\frac{1}{18}$

$\text{(2) 1 on die-1 and 3 on die-2.}
\;\;\;P(\text{1 die-1}) \,=\,\frac{1}{6}
\;\;\;P(\text{3 die-2}) \,=\,\frac{1}{6}
P(\text{1 die-1 }\wedge\text{ 3 die-2}) \:=\:\frac{1}{6}\,\cdot\frac{1}{6}\:=\:\frac{1}{36 }$

$P(\text{3 on one die, 1 on the other}) \:=\:\frac{1}{18}\,+\,\frac{1}{36} \:=\:\frac{1}{12}$

Quote:
 Draw a 2-way table to illustrate all possible totals when both dice are thrown.

[color=beige]. . [/color]$\begin{array}{c|cccccc}
& 1&1&2&3&6&6 \\\\ \hline
1 & 2&2&3&4&7&7 \\ \\
2 & 3&3&4&5&8&8\\ \\
3 & 4&4&5&6&9&9 \\ \\
4 & 5&5&6&7&10&10 \\ \\
5 & 6&6&7&8&11&11 \\ \\
6 & 7&7&8&9&12&12 \end{array}$

 February 9th, 2014, 04:06 PM #4 Newbie   Joined: Oct 2013 Posts: 8 Thanks: 0 Re: Probability of 2 dice and grid/table? Thank-you for the reply(s) I really profusely appreciate the help

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# probability two way tables for 2 dice

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