The political parties of a cube display numbers $2, 3, 3, 4, 4, 4$. Alice is rojo this cube threetimes. Find the probability that the an initial roll outcomes in an also number, and the sumof the numbers obtained from the second and third rolls is six.

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.



Did I do this correctly?

edited Jul 31 "20 at 20:13
asked Jul 31 "20 in ~ 18:53
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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 $6$


answered Jul 31 "20 at 19:18

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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
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