You are watching: Which of the following is the probability of rolling an even number

My Work: $\frac46\times\frac336=\frac118$

$\frac46$ = $4$ also numbers / $6$ possible outcomes

$3$ = amount of effective Outcomes when rolling a die twice ($2 + 4 = 6$ is one, $4 + 2 = 6$ is another, and $3 + 3$ is the third)

$6^2 = 36$ possible outcomes/arrangements once rolling a die twice.

so$\frac336$

$\frac46\times\frac336=\frac118$

Did I do this correctly?

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edited Jul 31 "20 at 20:13

asked Jul 31 "20 in ~ 18:53

user812532user812532

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## 2 answers 2

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Yes, $4$ faces out of $6$ have actually an also number, therefore you space correct on the an initial roll being even having probability $\frac46$.

Your analysis about the second and third rolls having a amount of $6$ is not correct.

One means is to roll a $2$, then roll a $4$. This has actually probability $\frac16\times\frac36=\frac336=\frac112$

Another is to roll a $4$, then roll a $2$. This has probability $\frac36\times\frac16=\frac336=\frac112$

Finally, you can roll a $3$, followed by an additional $3$. This has probability $\frac26\times\frac26=\frac436=\frac19$

The all at once probability of rolfes $2$ and $3$ having a sum of $6$ is the amount of those probabilities.$\frac336+\frac336+\frac436=\frac1036=\frac518$

To answer your question, main point the probability of first roll also by the probability the the second and 3rd rolls having actually sum of $6$

$\frac46\times\frac518=\frac20108=\frac527$

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answered Jul 31 "20 at 19:18

DreiCleanerDreiCleaner

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Yes, $\frac 46$ is the probability that getting even number in the first throw.

Also as you have mentioned, you can acquire sum of 6 from the following two throws as $4+2$, $2+4$ and $3+3$. But in a throw, probability of obtaining a $4$ is $\frac 36$, of acquiring a $3$ is $\frac 26$ and also of gaining a $2$ is $\frac 16$.

So the probability of getting a amount of six from next two litter = $2.\frac 36.\frac 16 + \frac 26.\frac 26 = \frac 518$

Now you can multiply by $\frac 46$.

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answered Jul 31 "20 in ~ 19:19

snucongo.org Loversnucongo.org Lover

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