# Probability

• Feb 3rd 2008, 07:29 AM
taypez
Probability
Poker dice is played by simultaneously rolling 5 dice.

a) Describe the sample space S; how many points are there?

6^5=7776 Is this correct?

b) Show that P(no two dice show the same number) = .0926

I know I need to use 1-P(A) and P(A) is the prob that two dice show the same number.

How do I find P(A)?

Thanks
• Feb 3rd 2008, 08:04 AM
Soroban
Hello, taypez!

Quote:

Poker dice is played by simultaneously rolling 5 dice.

a) Describe the sample space S; how many points are there?

. . $\displaystyle 6^5\:=\:7776$ . Is this correct? . . . . . Yes!

Quote:

b) Show that: .$\displaystyle P(\text{no two dice show the same number}) \:= \:0.0926$

I know I need to use 1 - P(A) . . . . . no

We can solve this head-on . . .

$\displaystyle \begin{array}{cc}\text{The first die can have any number:} &\frac{6}{6}\\ \text{The 2nd die must not have the first number:} & \quad\frac{5}{6} \\ \text{The 3rd die must not have the first two numbers:} & \qquad\frac{4}{6} \\ \text{The 4th die must not have the first three numbers:} & \qquad\quad\frac{3}{6} \end{array}$
$\displaystyle \begin{array}{cc}\text{The 5th die must not have the first four numbers:} & \qquad\qquad\frac{2}{6} \end{array}$

Therefore: .$\displaystyle P(\text{no two dice show the same number}) \;=\;\frac{6!}{6^5} \;=\;0.0\overline{925}$