Question

Consider all numbers between 0 and 99, inclusive. We define the following two events:

Event g: The number is divisible by 4
Event h: The number is divisible by 5

Problem 1: Write out the space for g and h, i.e., write out which numbers between 0 and 99 belong to g and h.

Problem 2: Find P(g) and P(h).

Problem 3: Are the events g and h exclusive? Explain.

Problem 4: Find P(g or h).

Answer 1

The space for events g and h consists of numbers between 0 and 99 that are divisible by 4 and 5, respectively. The probabilities P(g) and P(h) are 0.25 and 0.20, events g and h are not exclusive, and P(g or h) is 0.44.

Step-by-step explanation:

Probability of Divisible Numbers

Considering all numbers between 0 and 99, inclusive:

Event g: The number is divisible by 4 (g = {0, 4, 8, ..., 96})

Event h: The number is divisible by 5 (h = {0, 5, 10, ..., 95})

The probability P(g) is calculated by counting how many numbers are divisible by 4 out of 100 and P(h) by how many numbers are divisible by 5 out of 100.

Problem 1 Solution: g = {0, 4, 8, ..., 96}; h = {0, 5, 10, ..., 95}

Problem 2 Solution: P(g) = 25/100 = 0.25; P(h) = 20/100 = 0.20

Problem 3 Solution: Events g and h are not exclusive because they share a number (0) that is divisible by both 4 and 5.

Problem 4 Solution: To find P(g or h), we add P(g) and P(h) and subtract P(g and h), getting P(g or h) = 0.25 + 0.20 - 0.01 = 0.44