Theoreticals probabilities and repeated events practice

Answer 1

1. A standard six-sided die is rolled repeatedly. What is the theoretical probability of rolling a 5 on any given roll?

Answer: The probability of rolling a 5 on a standard six-sided die is 1/6 or approximately 0.1667.

2. A coin is flipped 3 times. What is the theoretical probability of getting exactly 2 heads?

Answer: The theoretical probability of getting exactly 2 heads in 3 coin flips can be calculated by using the binomial probability formula: P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful outcomes (heads), and p is the probability of success on each trial (0.5 for a fair coin). Plugging in the values, we get P(X=2) = (3 choose 2) * (0.5)^2 * (0.5)^(3-2) = 3 * 0.25 * 0.5 = 0.375.

3. A bag contains 5 red marbles and 3 blue marbles. If a marble is randomly selected from the bag, what is the theoretical probability of selecting a red marble?

Answer: The theoretical probability of selecting a red marble can be calculated by dividing the number of red marbles by the total number of marbles in the bag: P(red) = 5/8 = 0.625.

4. A deck of 52 cards is shuffled and a card is drawn. What is the theoretical probability of drawing a club?

Answer: The theoretical probability of drawing a club can be calculated by dividing the number of clubs in the deck by the total number of cards: P(club) = 13/52 = 0.25.

5. A spinner with 8 equal sections numbered 1-8 is spun 4 times. What is the theoretical probability of spinning a 3 on each spin?

Answer: The theoretical probability of spinning a 3 on each spin is (1/8) * (1/8) * (1/8) * (1/8) = (1/8)^4 = 1/4096 or approximately 0.00024.