There are 4 queens in a deck of 52 cards. Probability = 4/52 = 1/13.

There are 26 red cards (hearts and diamonds). The probability of drawing a heart given that the card is red is 13/26 = 1/2.

There are 13 hearts in a deck of 52 cards. The probability of drawing a heart is 13/52 = 1/4.

Using the formula for the radius of the incircle r = A/s, where A is the area and s is the semi-perimeter.

Using the distance formula, the radius can be calculated from the center found using the circumcircle method.

Numbers greater than 4 are 5 and 6. Probability = 2/6 = 1/3.

The possible outcomes greater than 2 are {3, 4, 5, 6}. The even numbers among these are {4, 6}. Thus, the probability is 2/4 = 1/2.

Even numbers on a die: 2, 4, 6. Probability = 3/6 = 1/2.

The possible outcomes greater than 2 are {3, 4, 5, 6}. The even numbers among these are {4, 6}. Thus, the probability is 2/3.

The possible combinations of children are BB, BG, GB, GG. Given that at least one is a boy, we can eliminate GG, leaving us with BB, BG, GB. Out of these 3 combinations, only 1 is BB. Therefore, the probability is 1/3.

The possible combinations are BB, BG, GB. Given at least one is a boy, the combinations are BB, BG, GB. The probability of both being boys is 1/3.

The possible combinations of children are BB, BG, GB, GG. Out of these, only 1 combination is both boys (BB). Thus, the probability is 1/4.

The only combinations with at least one boy are: BBB, BBG, BGB, GBB, BGG, GBG, GGB. Out of these, all combinations except BBB have at least one girl. Thus, P(At least one girl | At least one boy) = 6/7.

Total marbles = 4 + 5 + 6 = 15. Non-blue marbles = 4 + 5 = 9. Probability = 9/15 = 3/5.

Total marbles = 4 + 5 + 6 = 15. Probability of red or green = (4 + 5)/15 = 9/15 = 3/5.

Total marbles = 4 + 5 + 6 = 15. Probability of green = 5/15 = 1/3.

The total number of marbles is 4 + 5 + 6 = 15. The probability of picking a green marble is 5/15 = 1/3.

The total number of marbles is 4 + 5 + 6 = 15. The probability of selecting a green marble is 5/15 = 1/3.

Total marbles = 5 + 3 + 2 = 10. Favorable outcomes (red or green) = 5 + 3 = 8. Probability = 8/10 = 4/5.

Total marbles = 5 + 3 + 2 = 10. Probability of green = 3/10.

The total number of marbles is 5 + 3 + 2 = 10. The number of favorable outcomes (red or green) is 5 + 3 = 8. Thus, the probability is 8/10 = 4/5.

Using tan(30°) = height/distance, we have 1/√3 = 100/distance. Therefore, distance = 100√3 ≈ 173.2 m.

Using tan(30°) = 100/distance, we have 1/√3 = 100/distance. Therefore, distance = 100√3 ≈ 173.21 m.

Using tan(60°) = height/distance, we have distance = height/tan(60°) = 30/√3 = 15√3 m.

Using tan(45°) = height/distance, we have 1 = 30/distance. Therefore, distance = 30 m.

Distance = height / tan(angle) = 50 / (1/√3) = 50√3 meters.

Using sin(θ) = opposite/hypotenuse, we have sin(θ) = 8/10. Therefore, θ = sin⁻¹(0.8) ≈ 53.13 degrees.

Using sin(θ) = opposite/hypotenuse, we have sin(θ) = 12/15. Therefore, θ = sin⁻¹(0.8) ≈ 53.13 degrees.

Using sin(60°) = height/hypotenuse, we find the height = 12 * tan(60°) = 12√3 m.

Using tan(45°) = height/distance, we have height = distance * tan(45°) = 100 * 1 = 100 m.