Q1. Total outcomes = 90. (i) Two-digit numbers = 81, $P = 9/10. (ii) Perfect squares (1 to 81) = 9, $P = 1/10. (iii) Divisible by 5 = 18, $P = 1/5$.
Q2. Total cards = 52. (i) Red kings = 2, $P = 1/26. (ii) Face cards = 12, $P = 3/13. (iii) Red face cards = 6, $P = 3/26. (iv) Jack of hearts = 1, $P = 1/52. (v) Spade = 13, $P = 1/4. (vi) Queen of diamonds = 1, $P = 1/52$.
Q3. Winning outcomes (HHH, TTT) = 2. Losing outcomes = 6. Probability of losing = $6/8 = 3/4$.
Q4. Total outcomes = 36. (i) Sum is 8 (5 outcomes), $P = 5/36. (ii) Sum is 13 (0 outcomes), $P = 0. (iii) Sum $ \le 12$ (36 outcomes), $P = 1$.
Q5. Theoretical probability is based on equally likely outcomes ($P = N_e / N_t$). Experimental is based on actual trials of an experiment.
