Probability

The probability of getting 4, 5, or 6 on one die is 3/6 = 1/2. The probability of getting 1, 2, 3, or 4 on the second die is 4/6 = 2/3. Since the events are independent, the joint probability is (1/2) * (2/3) = 1/3.

A die has 6 faces: {1, 2, 3, 4, 5, 6}. Even numbers are {2, 4, 6}. Probability = 3/6 = 1/2.

A fair coin has two equally likely outcomes: heads and tails. The probability of getting a head is the number of favorable outcomes (1) divided by the total number of outcomes (2).

Total numbers from 3 to 100 is 100 - 3 + 1 = 98. Multiples of 7 are 7, 14, ..., 98. This is 7*1 to 7*14, so there are 14 multiples. Probability = 14/98 = 1/7.

A standard deck has 52 cards, with 13 cards of each suit. The probability of drawing a club is 13/52 = 1/4.

There are 52 cards in a deck. There are two red suits (hearts and diamonds), and each has one queen. Thus, there are 2 red queens. The probability is 2/52, which simplifies to 1/26.

Total outcomes = 36. Outcomes with exactly one 5: (5,1), (5,2), (5,3), (5,4), (5,6), (1,5), (2,5), (3,5), (4,5), (6,5). There are 10 such outcomes. Probability = 10/36 = 5/18.

A single coin toss results in either a head or a tail, but not both simultaneously. Therefore, the probability of getting both a head and a tail in one toss is 0.

A fair coin has two equally likely outcomes: heads or tails. The probability of heads is the number of favorable outcomes divided by total outcomes, which is 1/2.

Total outcomes for 3 coins = 2^3 = 8. Outcomes with 1 head and 2 tails are (HTT, THT, TTH), which is 3 outcomes. Probability = 3/8.

The experimental probability from 80 tosses is 14/80 = 7/40. The question asks for the probability of getting 3 when a die is tossed at random, which is a theoretical probability of 1/6. Given the options, the question likely expects the experimental probability derived from the provided data.

Total outcomes = 2^5 = 32. Favorable outcomes (2 heads) = 5C2 = 10. Probability = 10/32 = 5/16.

The probability of getting no head in one toss is 1/2. For five tosses, it is (1/2)^5 = 1/32.

Total outcomes for two dice = 36. Sum of 5 can be (1,4), (2,3), (3,2), (4,1) -> 4 outcomes. Probability = 4/36 = 1/9.

Initial blue probability 1/5 = 8/(15+8+G), so 15+8+G = 40, G = 17. After removing 5 green marbles, green count is 12 and total is 35. Probability of green is 12/35.