Probability

Total outcomes for 4 tosses = 2^4 = 16. Outcomes with exactly 3 tails: (T,T,T,H), (T,T,H,T), (T,H,T,T), (H,T,T,T). There are 4 such outcomes. Probability = 4/16 = 1/4.

Total outcomes = 36. Sum > 6: (1,6), (2,5), (2,6), (3,4), (3,5), (3,6), (4,3), (4,4), (4,5), (4,6), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6). Total = 21 outcomes. Probability = 21/36 = 7/12.

Numbers divisible by 3: 3, 6, 9, 12, 15 (5 numbers). Numbers divisible by 7: 7, 14 (2 numbers). No overlap. Total = 7 numbers. Probability = 7/17.

Total outcomes = 36. Prime sums are 2, 3, 5, 7, 11. Counts: 2(1), 3(2), 5(4), 7(6), 11(2). Total = 1+2+4+6+2 = 15. Probability = 15/36 = 5/12.

Total balls = 10. Probability of picking the first red ball is 8/10. Probability of picking the second red ball is 7/9. Total probability = (8/10) * (7/9) = 56/90 = 0.622. The option 0.6 is the closest approximation.

There are 13 Hearts and 4 Kings in a deck. One King is also a Heart, so there are 13 + 3 = 16 unique cards that are either a King or a Heart. The probability is 16/52.

Total balls = 9 (2P, 3Br, 4Bl). Total ways to pick 3 = C(9, 3) = 84. Ways with no brown balls = C(6, 3) = 20. Ways with at least one brown = 84 - 20 = 64.

Total arrangements = 16! / (10! * 2! * 4!). 16! / (10! * 2 * 24) = (16 * 15 * 14 * 13 * 12 * 11) / 48 = 120120.

Total outcomes = 6^3 = 216. Sum of 16: (6,6,4) in 3 ways, (6,5,5) in 3 ways. Total ways = 6. Probability = 6/216 = 1/36.

Total balls = 15. Odd balls = {1, 3, 5, 7, 9, 11, 13, 15} (8 balls). Probability = (8/15) * (7/14) * (6/13) = (8/15) * (1/2) * (6/13) = 4/15 * 6/13 = 24/195 = 8/65.