For the problem regarding an independent event, how can we know that the formula P(A and B) = P(A). P(B), applies to a particular situation or not ? As for an example, a problem is given below. Why can’t we apply the aforementioned formula to get the desired result in this problem ? (The formula would give P(A and B) = 24/15*15, which actually is 2/15 as in the solution below)

PROBLEM: A 15-sided die, with faces numbered 1 to 15 is to be rolled once, and

each of the 15 possible outcomes is equally likely to occur.

The probability of rolling a number that is either a multiple of 5 (that is, rolling a 5, 10 or a 15) or an odd number (that is, rolling a 1, 3, 5, 7, 9, 11, 13, or 15) is equal to what fraction?

SOLUTION: P(multiple of 5) + P(odd) - P(multiple of 5 and odd)

= 3/15 + 8/15 - 2/15

= 9/15