Probability

A die has outcomes {1, 2, 3, 4, 5, 6}. Even numbers are {2, 4, 6}. Not getting an even number means getting {1, 3, 5}. The probability is 3/6 = 1/2.

Let total beads be T. Green = T/3, Pink = T/4. White = 10. T/3 + T/4 + 10 = T. 7T/12 + 10 = T. 10 = 5T/12. T = 24.

Total outcomes for 3 coins = 2^3 = 8. Outcomes with at least two heads: HHH, HHT, HTH, THH. Total = 4. Probability = 4/8 = 1/2. Since 1/2 is not listed, 'None of these' is correct.

The probability of not getting a 4 in one throw is 5/6. For two throws, the probability of never getting a 4 is (5/6) * (5/6) = 25/36. Thus, the probability of getting at least one 4 is 1 - 25/36 = 11/36.

A die has 6 faces {1, 2, 3, 4, 5, 6}. Numbers lesser than 4 are {1, 2, 3}. Probability = 3/6 = 1/2.

Total ways to draw 2 cards = 52C2 = (52*51)/2 = 1326. Ways to draw 2 kings = 4C2 = 6. Probability = 6/1326 = 1/221.

Total outcomes = 2^3 = 8. Outcomes with at most two heads are all except (H,H,H). There is only 1 outcome with three heads. So, 8 - 1 = 7 favorable outcomes. Probability = 7/8.

Total outcomes = 6^3 = 216. Triplets are (1,1,1), (2,2,2), (3,3,3), (4,4,4), (5,5,5), (6,6,6), which is 6 outcomes. Probability = 6/216 = 1/36.

A die tossed twice has 36 outcomes. Sum of 10 can be achieved by (4,6), (5,5), (6,4). There are 3 favorable outcomes. Probability = 3/36 = 1/12.

Total balls = 4 red + 2 yellow = 6. Probability of red = (Number of red) / (Total balls) = 4 / 6 = 2/3.

A fair coin has two outcomes, heads and tails. Each team has an equal probability of 1/2 of starting the game.

Total tosses = 100. Heads = 59. Tails = 100 - 59 = 41. Probability of tail = 41/100.

A die has 6 faces: {1, 2, 3, 4, 5, 6}. The outcomes less than 4 are {1, 2, 3}. The probability is 3/6 = 1/2.