1.A container holds 3 blue, 4 red, 6 green, and 2 yellow marbles. If you randomly select four marbles, what is the probability that no blue marble is chosen?
2.A box contains 9 bulbs, of which 4 are faulty. If 4 bulbs are selected randomly, what is the probability that there is at least one working bulb among them?
3.A total of nine bulbs are in a box, with four of them being faulty. If you randomly select four bulbs, what is the probability that every bulb chosen is defective?
4.If three standard six-sided dice are rolled simultaneously, what is the probability that exactly two of them display the same number?
5.If three standard six-sided dice are rolled simultaneously, what is the probability that all three dice display distinct numbers?
6.If three standard six-sided dice are rolled simultaneously, what is the probability that all three dice display the same number?
7.A basket contains 5 apples and 4 oranges. If three fruits are selected randomly, what is the probability that the selection includes at least two apples?
8.A bag contains 7 green balls and 8 white balls. If two balls are picked at the same time, what is the probability that both balls are of the same color?
9.What is the probability that three specific individuals always sit together when six people are arranged in a row?
10.What is the probability of selecting either a spade or a king from a standard, well-shuffled deck of cards?
11.When tossing four coins, what is the probability of obtaining exactly two heads and two tails?
12.When rolling two dice simultaneously, what is the probability that one die shows an even number while the other shows an odd number?
13.A number is randomly chosen from the first 20 natural numbers. What is the probability that the selected number is either even or prime?
14.What is the probability of randomly selecting a perfect cube from the numbers 1 through 100?
15.A fair coin is flipped five times. What is the probability of getting at least one tail in these five tosses?
16.What is the probability that a randomly chosen number from the first 50 natural numbers is a composite number?
17.Three taps A, B, and C can fill a tank in 12, 15, and 20 hours respectively. If tap A runs continuously while taps B and C operate alternately for one hour each, how long will it take to fill the tank completely?
18.A tank can be filled by one tap in 4 hours, while another tap can drain it in 9 hours. If both taps are opened at the same time, how long will it take to fill the tank completely?
19.A single tap can fill a tank in 6 hours. Once the tank is half full, three additional identical taps are opened. How long will it take to fill the tank entirely?
20.A large tanker can be filled by pipe A alone in 60 minutes and by pipe B alone in 40 minutes. If pipe B runs for half the total filling time and then both pipes A and B operate together for the remaining half, how long will it take to fill the tanker completely from empty?