Upon rolling an irregular die, the probability of getting the numbers , and 5 are equal, and that of getting the number 6 is three times the probability of getting the number 1.
Calculate the probability of getting an odd prime number.
In this case, events , , , , and are getting the
numbers 1, 2, 3, 4, and 5, respectively, and event is getting
the number 6. Suppose the probability of each of the events ,
, , , and is . The probability of event would
then be .
Since events , , , , , and are mutually
exclusive, and they make up the sample space, the sum of their
probabilities must be equal to 1. First, use this fact to find the
value of as follows:
The odd prime numbers are 3 and 5, which are represented by events
and . Also, the notation refers to the
probability of either event or event occurring. If and
are two mutually exclusive events, then . Now use this fact to determine as follows: