Probability and Statistics Outcomes and Events

all right let's take look at this problem break it down Jeremy throws two tetrahedral base dice and dice he takes note of the number on the underside of each die and calculates their product so he's throwing four-sided dice he's going to throw this dice in this dice he's going to look at the two numbers that he got and then he's going to get their product by multiplying those two values together now four-sided dice means that we have values of one two three and four and the other dice is also going to have values of one two three and four and we're going to be finding their products so we can make chart here just like this and we can find all of our possible outcomes one times one is going to give me one one times two two three four two three four two times two is four two times three six two times four is eight two times three is six two times four is eight three times three is nine three times four is twelve four times four sixteen and we're gonna get another 12 right there so by making this chart right here we got one two three or four on one dice one two three or four on the other dice now we can see every possible outcome everything we're looking at here are possible outcomes for product now if we can look at this chart we should be able to answer which one of these events is certain to occur meaning it has to happen Okay so product is square number square numbers are like four nine then sixteen but notice we could get six we could get three those are not square numbers so is off the table it's not event two product is cube number our numbers are like one eight six excuse me not sixteen twenty seven there's some Cube numbers right there we could get an 27 is not on there ones yeah so there's all these other possible outcomes that went work for event number two event number three product is factor of 144. well one thing can tell you about 144 is it's divisible by lot of different values right so what you could do right here is just take calculator take 144 and start dividing it by the ones that you're not sure of you obviously know that it can be divisible by two right it's an even value so we can cut it in half no problem but as you go through this list and you use all those numbers in there what you're going to realize is every single one of those is going to be factor of 144. so it's looking at me like is the correct answer but let's double check event four just to make sure here we go product is either prime number or composite number product is either prime number or composite number gut tells me that that's true too right it would be if that was not possible outcome one is not Prime and it is not composite it is neither so because of that value of one is also not correct so it's kind of tricky problem because lot of you might look at this bottom answer it might go with okay but the reason is incorrect is because 1 is not prime one is also not composite number study hard and good luck on your upcoming test