8.6 Miscellaneous

8.6.1 Misc Problem #01

What is the probability that in a leap year, there are 53 Fridays?

  • In a leap year, there are 366 days, i.e., 52 weeks and 2 days. In each week is a Fridays, so there are no less than 52 Fridays. The remaining two days could be:
  • (Sat, Sun); (Sun, Mon); (Mon, Tue); (Tue, Wedn); (Wedn, Thu); (Thu, Fri); (Fri, Sat) = 7
  • Total possible outcome = 7 and favorable outcomes = 2
  • \(P = \frac{2}{7}\)

8.6.2 Misc Problem #02

Out of the natural numbers 10 through 30, a number is chosen randomly; what is the probability that the number is

  1. a prime number
  2. a prime number or multiple of 5
  3. a prime number or an odd number
  4. not a perfect square

8.6.3 Misc Problem #03

What is the probability that the product of three positive integers chosen from 1 through 100 is an even number?

  • Three possible cases
  • All three are even
  • Two odd and one even number
  • Two even and one odd
  • \(P=\frac{^{50}C_3}{^{100}C_3}+...\)
  • 0.88