Aman and Bhuvan throw a pair of dice alternately, and whoever first gets a sum of 8 wins. Find each player’s probability of winning if Aman starts, using an infinite geometric series.
NCERT Class 11 Probability Ex 11.2 Q21: 60 students, 30 in NCC, 32 in NSS, 24 in both — find P(NCC or NSS), P(neither) and P(NSS but not NCC).
A girl throws a die: on 5 or 6 she tosses a coin 3 times, otherwise once. Given she got exactly one head, find the probability she threw 1, 2, 3, or 4, using Bayes’ theorem.
A box has 4 red and 5 black marbles. Find the probability distribution of the number of red marbles in a random draw of 3, then its mean and standard deviation.
Bag 1 has 6 green, 3 red balls; Bag 2 has 5 green, 4 red. One ball moves from Bag 1 to Bag 2, then one is drawn from Bag 2. Find the probability it’s red.
A construction job has 0.65 probability of a strike, with different completion probabilities depending on whether there’s a strike. Find the overall probability of on-time completion using total probability.
A committee of 4 is chosen from 8 boys and 6 girls, with at least one girl. Find the probability the committee has more girls than boys, using conditional probability.
Two dice are rolled once. Find the probability of getting an even number on the first die or a total of 8, using the addition rule for probability.
A derivation of P(A∪B)=1−P(A’)P(B’) for independent events A and B, from NCERT Example 14, using the standard union and complement rules.
A 2×2 matrix has entries from {0,1}. Let X be its determinant. Find the variance of X by listing all 16 matrices and their determinant probabilities.