25-42 ■ Probability These exercises involve probability.
Divisors of a Number Let . (Note that .)
(a) How many divisors does N have?
(b) How many even divisors does have?
(c) How many divisors of are multiples of ?
(d) What is the probability that a randomly chosen divisor of is even?
The number of divisors of .
The number is
The total number of divisors of a number is given by,
The number of even divisors of .
The number of divisors that are multiples of .
The probability that a randomly chosen divisor of is even.
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