BStat BMath UGA 2024 Quiz

Explore essential probability, statistics, and mathematics concepts relevant to the BStat and BMath entrance exams at UGA 2024. Sharpen your problem-solving skills with practical questions reflecting the exam's core focus areas.

1. Probability Fundamentals

   In a bag containing 7 red and 5 blue balls, what is the probability of drawing a red ball in a single random pick?

   1. 7/12
   2. 5/12
   3. 5/7
   4. 12/7

   Explanation: The probability of drawing a red ball is the number of red balls divided by the total number of balls, so 7/12 is correct. 5/12 represents the probability of drawing a blue ball, not red. 5/7 incorrectly reverses numerator and denominator. 12/7 is an invalid probability as it exceeds 1.

2. Combinatorics

   How many different four-digit numbers can be formed using the digits 1, 2, 3, and 4 with each digit used exactly once?

   1. 16
   2. 42
   3. 12
   4. 24

   Explanation: There are 4! = 24 ways to arrange four unique digits, making 24 the correct answer. 16 and 12 are both too low and might come from miscalculating permutations. 42 is too high and could result from multiplying in more digits or positions than actually used.

3. Set Theory

   If A and B are two sets with |A| = 5, |B| = 8, and their intersection has 2 elements, how many elements are in their union?

   1. 11
   2. 15
   3. 13
   4. 10

   Explanation: The union is calculated as |A| + |B| - |A ∩ B| = 5 + 8 - 2 = 11. 10 arises from incorrect subtraction or overlap calculation. 15 incorrectly adds the total elements without considering intersection. 13 ignores proper overlap adjustment.

4. Functions and Relations

   Consider the function f(x) = x^2 - 4x + 5. What is the minimum value of f(x) for real values of x?

   1. -5
   2. 4
   3. 1
   4. 5

   Explanation: The function achieves its minimum at the vertex, x = 2; plugging this in gives f(2) = 4 - 8 + 5 = 1. -5 is not achievable for this quadratic since it's always positive. 5 and 4 are function values at other points, not the minimum.

5. Descriptive Statistics

   Given the dataset: 2, 4, 6, 8, 10, what is the standard deviation?

   1. 2
   2. 4
   3. 3.16
   4. 2.83

   Explanation: The mean is 6, and calculating the variance and then the square root yields approximately 2.83. 2 is the average difference from the mean, not the standard deviation. 3.16 is a common confusion with root ten. 4 overestimates the spread.