Two number cubes are rolled. Find the probability of each outcome. The sum of the numbers rolled

Two number cubes are rolled. Find the probability of each...

Key Concepts

Sample Space

The sample space is the complete set of all possible outcomes of a random experiment. In the context of rolling two dice, the sample space includes every ordered pair representing the result of each die, and knowing its size is crucial for calculating probabilities.

Favorable Outcomes

Favorable outcomes refer to the subset of the sample space that corresponds to the event of interest. When calculating the probability of a particular event, such as obtaining a specific sum, it is essential to identify all outcome combinations that satisfy the event's condition.

Probability

Probability is a measure that quantifies the chance of an event occurring, expressed as the ratio of favorable outcomes to the total number of possible outcomes. This concept is foundational in understanding how likely an event is, such as obtaining a certain sum when rolling dice.

Transcript

00:04 All right.

00:05 So in this problem, similar to the last problem, we are doing the spiral review questions.

00:11 And this one is asking, if you were to roll two number cubes, also called dice, in different kinds of games, what would be the probability of a certain event happening? in my previous example, which i recommend that you go back to if you are a little bit unsure about what types of questions might be asked for probability.

00:34 In this situation, we're looking for the probability that if you were to roll two different number die or cubes, and you were to add the result of their rolls, what would be the probability that the sum is five? and a probability is the likelihood that something would happen as a fraction or percentage of the total event space.

00:59 So in this situation, the different possible outcomes for the first dye, which i've notated as a white dye, so i can keep track of the two, is either a one, two, three, four, five, or six, because most number cubes that are in different kinds of games are a six -sided die.

01:22 You also have the other die getting a one, two, three, four, five, or six.

01:27 But each of those are then paired together.

01:29 So you could get a one with a one, a one with a two, a one with a three, and so on.

01:35 But then you can also get a two with a one, which is different than a one with a two.

01:41 And so each of those are different events.

01:43 Altogether, the space in between inside of this table that i've created, there are 36 possible outcomes.

01:52 And each of those has a different sum.

01:54 So let's go ahead and find the sum of a few of them.

01:57 And then we can just see if we're in the right space or not.

02:02 So the sum of the first two would be if you get a one and a one, you have a sum of two.

02:07 A one and a two, that gives you a sum of three.

02:10 A sum of one and three, that gives you a four.

02:13 A sum of one and four, that gives you five.

02:15 And the next one would be six...

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