## 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