Question

Let the sample space be S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose that the outcomes are equally likely. Compute the probability of the event.

Answer 1

To calculate the probability of an event, divide the number of favorable outcomes by the total number of outcomes in the sample space. In a dice example where event A is getting an even number, P(A) would be 1/2. If event E is rolling a number at least five, then P(E) is 1/3.

Step-by-step explanation:

To calculate the probability of an event when all outcomes in the sample space are equally likely, you need to divide the number of favorable outcomes by the total number of outcomes in the sample space.

For example, in a sample space S = {1, 2, 3, 4, 5, 6}, if event A represents rolling a number that is even, then A = {2, 4, 6}. To find P(A), you would calculate 3 (the number of even outcomes) divided by 6 (the total number of outcomes in S), resulting in P(A) = 1/2.

For a more concrete example, if we have an event E which is rolling a number at least five, then E = {5, 6}, and P(E) would be 2 (number of outcomes in event E) divided by 6 (total outcomes in S), giving us P(E) = 1/3.