题目内容

Assume we roll 2 four sided dice. What is P({rolling a 2 and a 3, in any order})? Answer in reduced fraction form - eg 1/5 instead of 2/10.______

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Assume we roll 2 four sided dice. What is P({rolling a 2 followed by a 3})? Answer in reduced fraction form - eg 1/5 instead of 2/10.______

Assume we roll 2 four sided dice. What is P({sum of the rolls is even})? Answer in reduced fraction form - eg 1/5 instead of 2/10.______

What is the size of the sample space for two rolls of a four sided die?______

In this problem, we're going to calculate some probabilities of dice rolls. Imagine you have two fair four-sided dice (if you've never seen one, here's a picture. The result, a number between 1 and 4, is displayed at the top of the die on each of the 3 visible sides). 'Fair' here means that there is equal probability of rolling any of the four numbers.You can answer the following questions in one of two ways - you can calculate the probability directly, or, if you're having trouble, you can simply write out the entire sample space for the problem. A sample space is defined as a listing of all possible outcomes of a problem, and it can be written in many ways - a tree or a grid are popular options. For example, here is a diagram of the sample space for 3 coin tosses.Some vocabulary before we begin: an event is a subset of the sample space, or, a collection of possible outcomes. A probability function assigns an event, A, a probability P(A) that represents the likelihood of event A occuring.As an example, let's say we flip a coin. Define the event H as the event that the coin comes up heads. We can assign the probability P(H) = 1/2; the likelihood that event H occurs.The following problems will ask for the probability that a given event occurs.What is the size of the sample space for one roll of a four sided die?______