There is a bag with three balls numbered 1 to 3. There is also a pack of three cards lettered K, Q, and J.As a trial of an experiment, a ball was chosen and a card drawn. The number 1 to 3 of the ball and the letter K, Q, or J of the card drawn were recorded.Here is a summary of the data from 825 trials.Outcome 1K 2K 3K 1Q 2Q 3Q 1J 2J 3JNumber of trials 94 96 85 99 93 85 83 94 96Answer each part.(a) Assuming the ball was chosen and the card was drawn at random, find the theoretical probability of this event: both choosing the 2 or 3 ball and drawing a Q or J card, in a single trial. Round your answer to the nearest thousandth.(b) Use the data to find the experimental probability of this event: both choosing the 2 or 3 ball and drawing a Q or J card, in a single trial. Round your answer to the nearest thousandth.(c) Choose the statement that is true.The experimental probability will never be very close to the theoretical probability, no matter the number of trials.The smaller the number of trials, the greater the likelihood that the experimental probability will be close to the theoretical probability.The larger the number of trials, the greater the likelihood that the experimental probability will be close to the theoretical probability.

A bag has six balls labeled A, B, C, D, E and F. One ball will be randomly picked, and its letter will be recorded as the outcome. Give all of the outcomes for the event of choosing a letter from C to F. If there is more than one element in the set, separate them with commas.2 points{A, B, C, D}{A, B, C, D, E}{A, B C, D, E, F}{C, D, E, F}

A bag has six balls labeled A, B, C, D, E and F. One ball will be randomly picked, and its letter will be recorded as the outcome. Give the sample space describing all possible outcomes.2 points{A, B, C, D}{A, B, C, D, E}{A, B C, D, E, F}{A, B, C}

A bag two blue balls and three pink balls. A ball is selected from the bag at random but not replaced. A second ball is then drawn, and again, not replaced. Use a tree diagram to determine the sample space. (3 marks)

ProbabilityA bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:Options1/311/342/911/92

There is a pack of four cards numbered 1 to 4. There is also a coin with one side marked as heads and the other tails.As a trial of an experiment, a card was drawn and the coin was flipped. The number 1 to 4 of the card and the side H for heads and T for tails of the coin from the flip were recorded.Here is a summary of the data from 550 trials.Outcome 1H 2H 3H 4H 1T 2T 3T 4TNumber of trials 73 73 66 65 69 74 66 64Answer each part.(a) Assuming the card was chosen at random and the coin is fair, find the theoretical probability of this event: both drawing the 2, 3, or 4 card and flipping heads, in a single trial. Round your answer to the nearest thousandth.(b) Use the data to find the experimental probability of this event: both drawing the 2, 3, or 4 card and flipping heads, in a single trial. Round your answer to the nearest thousandth.(c) Choose the statement that is true.With a large number of trials, there must be no difference between the experimental and theoretical probabilities.With a large number of trials, there might be a difference between the experimental and theoretical probabilities, but the difference should be small.With a large number of trials, there must be a large difference between the experimental and theoretical probabilities.