Assuming that each outcome is equally likely find the probab

Assuming that each outcome is equally likely, find the probability of each event in Exercise 6.

A die is called “balanced” or “fair” if each side is equally likely to land on top. Assign a probability to each outcome in the sample space for the experiment that consists of tossing a single fair die. Find the probabilities of the events E: “an even number is rolled” and T: “a number greater than two is rolled.”

Solution:

With outcomes labeled according to the number of dots on the top face of the die, the sample space is the set S={1,2,3,4,5,6}. Since there are six equally likely outcomes, which must add up to 1, each is assigned probability 1/6.

Since E={2,4,6}, P(E)=16+16+16=36=12.

Since T={3,4,5,6}, P(T)=46=23.

Solution

Yes, you are correct!

There are 6 elements in the sample space.

In event E, there are 3 of those. {2,4,6}

Hence, P(E) = 3/6 = 1/2 [answer]

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Here, {3,4,5,6}.

P(T) = 4/6 = 2/3 [answer]