a positive integer divisor of 12! is chosen at random. the probability that the di-visor chosen is a perfect square can be expre

Question

1 year ago

12

ssed asmn, wheremandnare relativelyprime positive integers. what ism n?

1 answer:

AveGali [126] · Answer 1 · 2024-01-18T06:55:55+03:00

The probability that the divisor chosen is a perfect square is found to be 1/22 which is m:n.

<h3>What exactly is meant by probability?</h3>

Probability is synonymous with possibility. It is a mathematical branch that deals with the occurrence of a random event.
The value ranges from zero to one. Probability has been introduced in mathematics to predict the likelihood of events occurring.

Given: Randomly, a positive integer divisor of 12! is selected.

Prime factorization of 12! = 2¹⁰ × 3⁵ × 5² × 7¹ × 11

Total divisors of 12! = 11 × 6 × 3 × 2 × 2

Each number in the prime factorization must have an even exponent in order to construct a perfect square divisor.
In the prime factorization, the divisor cannot have any factors of 7 and 11 because there is only one of each in 12!.
There are 6 × 3 × 2 perfect squares as a result.

The probability that the divisor chosen is a perfect square is given as:

(6 × 3 × 2)/(11 × 6 × 3 × 2 × 2)

= 1/22

=m/n

Therefore, the probability that the divisor chosen is a perfect square is found to be 1/22 which is m:n.

Learn more about probability here:

#SPJ4