Probability Question in NDA

Harmonic Mean & Combinations: You kick off by calculating the harmonic mean for a series of combination terms ($10C_3, 10C_4, 10C_5, 10C_6, 10C_7$). You demonstrate how to simplify these combinations using factorials and then apply the harmonic mean formula: $H = \frac{n}{\sum \frac{1}{x_i}}$. Independent Events: You solve a sample survey problem regarding farmers in debt. You explain that since the selection of each farmer is an independent event, the probability of all three being in debt is simply the product of their individual probabilities. Set Theory in Probability: Using the example of families owning laptops and desktops, you demonstrate the use of the Addition Rule for Probability: $P(L \cup D) = P(L) + P(D) - P(L \cap D)$ to find the probability of a family owning at least one device. Ball & Urn Problems: You cover classic selection problems involving drawing balls of different colors (white, red, blue) from a bag. You explain two methods for solving these: using the Combination method and the Multiplication method for sequential draws. Binomial Distribution: You briefly touch upon the specific conditions required to use a binomial distribution, such as having a finite number of trials, independent trials, and only two possible outcomes (success/failure). Contradiction & Truth-Telling: You solve a problem involving two people ($X$ and $Y$) who speak the truth with different frequencies. You explain that they "contradict" each other when one tells the truth and the other lies, leading to the sum of two scenarios: $(T_x \cap F_y) + (F_x \cap T_y)$. Permutations with Constraints: You address more complex scenarios, such as: Drawing specific colors from a die in a fixed order. Tossing a coin multiple times where no two "Heads" occur consecutively (using manual counting of favorable outcomes). Drawing numbers from a set that are not divisible by specific integers (5 or 9). Selecting two integers from 50 consecutive numbers such that their sum is odd (requiring one even and one odd number). #ndamaths #nda #ndaexam #probability #nda2026