5

12. If we roll a six-sided fair die three times and recordresults as an ordered list of length 3, how many of outcomescontain exactly one 2 or exactly one 5?...

Question

12. If we roll a six-sided fair die three times and recordresults as an ordered list of length 3, how many of outcomescontain exactly one 2 or exactly one 5?

12. If we roll a six-sided fair die three times and record results as an ordered list of length 3, how many of outcomes contain exactly one 2 or exactly one 5?



Answers

A die is rolled 12 times. Find the probabilities of rolling the following.
No more than 3 ones

So now in this, some were problem. We have to find probability off no more. Then three. What's so? Therefore we have enemies equals to 12 bees equals to one by six and our is either 01 two or three. So therefore we will, right? We can write it does 12 c zero one by six to the power of zero and five by six to be about off well, it is written or in by normal phone and we'll see one one by six to the power off one one minus one by six to the power off 11 and plus 12 c two one by six square When my six hold squared and one money that's one by six. Hold to the about off, then plus doing C three, which is one by six Whole cube on one minus one by six to de power off night. So if we solve them, our final probability is 0.7 four

So this problem is pretty similar to a true or false situation or heather tail situation. You throw dice, you only have so many options or availability. So in this case, we're trying to figure out the total number of outcomes that are possible. Um, if we were to toss five dies at the same time. So we're given that there's five dice, so we have to determine how many possible outcomes there are for one dice. So that's what's gonna go here. So we know that when you roll a regular standard, I, um, that there are six possible outcomes that you could roll. So then, if that's the case for five dies, it doesn't affect the other psychotically do six times six times, six times, six times six or raise it to the fifth power. And that's still applying the multiplication principle from this chapter. So six of the fifth power ends up being 7776 outcomes

There are six possible numbers you can roll when you will just one dice, and so for rolling five of them. That means we could do six times six times six times six times six. Or we could raise that to the five dice that are being thrown. You go on your calculator, you'll do six to the fifth power and you'll get 7776 possible outcomes.

If one dies is stole, we'll get six outcomes. And if fired eyes are rolled Hominy race off outcomes will come. Let's see. He first dies. Will roll. We'll get six art guns and second Ice also gives six outcomes on Third Dies. Also will give six outcomes on foot. Days also will give six art guns on even 50 days. Also abuse us six out guns. So if you multiply although six we'll get 777 six.


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