Question: What is the probability that a randomly selected integer chosen from the first 100 positive integers is odd?
12 chances are there for getting first 100 positive integer odd.
The probability that a randomly selected integer chosen from the first positive integers is odd is
As per the problem an integer is randomly chosen from first positive integers.
If S represents the sample space and E represents the event. Then the probability of occurrence of favourable event is given by the formula as given below:
Here we are choosing from the first positive integers so we have
The number of odd integers in the first positive integers are as follows
So, we have
Now substitute the values in the above formula we get
Question: Suppose that a Bayesian spam filter is trained on a set of 1000 spam messages and 400 messages that are not spam. The word “opportunity” appears in 175 spam messages and 2 messages that are not spam. Would an incoming message be rejected as spam if it contains the word “opportunity” and the threshold for rejecting a message is 0.9?
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