Probability of an event

**mathlete2** · February 22nd 2008, 02:33 PM

Suppose that two balanced dice are tossed repeatedly and the sum of the two uppermost faces is determined on each toss. What is the probability that we obtain
a) a sum of 3 before we obtain a sum of 7?
b) a sum of 4 before we obtain a sum of 7?

**Plato** · February 22nd 2008, 03:49 PM

Originally Posted by mathlete2

Suppose that two balanced dice are tossed repeatedly and the sum of the two uppermost faces is determined on each toss. What is the probability that we obtain
a) a sum of 3 before we obtain a sum of 7?

Consider the probabilities $P(3) = \frac{2}{{36}}\,\& \,P(7) = \frac{6}{{36}}$ .
In order for there to be a sum of three before a sum of seven happening on say the fifth toss we must have four sums of neither three nor seven and than a sum of three on the fifth toss. That probability is $\left( {\frac{{28}}{{36}}} \right)^4 \left( {\frac{2}{{36}}} \right)$ .

Will this work $\sum\limits_{k = 1}^\infty {\left( {\frac{{28}}{{36}}} \right)^{k - 1} \left( {\frac{2}{{36}}} \right)}$ ?

**Charbel** · February 23rd 2008, 12:57 AM

a sum of $x$ before a sum of $y$ on the $n$ th roll

$<br /> \left[ {1 - \left( {\frac{{ - \left| {y - 7} \right| - \left| {x - 7} \right| + 12}}<br /> {{36}}} \right)} \right]^{n - 1} \left[ {\frac{{ - \left| {x - 7} \right| + 6}}<br /> {{36}}} \right]<br />$

[Math]
x \in Z\cap {\left[ {2,12} \right]}
[/tex]
[Math]
y \in Z\cap {\left[ {2,12} \right]}
[/tex]
[Math]
n \in Z^+\cup \{0\}
[/tex]

lol?

**Plato** · February 23rd 2008, 04:02 AM

Not that $n \in Z^ + \, \mbox{not} \,n \in \left[ {Z^ + \cup \left\{ 0 \right\}} \right]$ .

**mathlete2** · February 23rd 2008, 08:45 AM

Well, see the answer is actually 1/4(a) and 1/3(b). I just don't know how they went about getting it?

**Plato** · February 23rd 2008, 09:36 AM

Originally Posted by mathlete2

Well, see the answer is actually 1/4(a) and 1/3(b). I just don't know how they went about getting it?

As you can plainly see that is exactly what I gave you for part (a).
Now you find how to do the part (b). Do somethings for yourself.

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