There is a number cube with faces numbered 1 to 6. There is also a coin with one side marked as heads and the other tails.As a trial of an experiment, the number cube was rolled and the coin flipped. The number 1 to 6 from the roll 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 110 trials.Outcome 1H 2H 3H 4H 5H 6H 1T 2T 3T 4T 5T 6TNumber of trials 7 9 12 10 5 6 12 9 13 8 10 9Answer each part.(a) Use the data to find the experimental probability of this event: both rolling a 1 or a 6 and flipping tails, in a single trial. Round your answer to the nearest thousandth.(b) Assuming the cube and the coin are fair, find the theoretical probability of this event: both rolling a 1 or a 6 and flipping tails, in a single trial. Round your answer to the nearest thousandth.(c) Choose the statement that is true.As the number of trials increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.The experimental and theoretical probabilities must always be equal.As the number of trials increases, we expect the experimental and theoretical probabilities to become farther apart.

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 60 trials.Outcome 1H 2H 3H 4H 1T 2T 3T 4TNumber of trials 5 7 9 11 5 10 6 7Answer each part.(a) Use the data to find the experimental probability of this event: both drawing the 1, 3, or 4 card and flipping heads, in a single trial. Round your answer to the nearest thousandth.(b) Assuming the card was chosen at random and the coin is fair, find the theoretical probability of this event: both drawing the 1, 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.

Leanne is conducting a probability experiment using a number cube with faces labeled from 1 to 6. Leanne rolled the number cube 40 times and recorded the number showing on top for each roll. The table shows the results. Number Cube ExperimentNumber Showing on Top Face Frequency1 72 93 64 35 76 8Based on these results, what is the experimental probability that the next time Leanne rolls the number cube that it will land with 1 or 6 showing on the top face?ResponsesA 585 8B 1151 15C 383 8D 26

number cube is rolled three times. An outcome is represented by a string of the sort OEE (meaning an odd number on the first roll, an even number on the second roll, and an even number on the third roll). The 8 outcomes are listed in the table below. Note that each outcome has the same probability.For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event.Outcomes ProbabilityEEE EOO OEE OEO EEO EOE OOO OOEEvent A: No even numbers on the last two rolls 18Event B: Two or more even numbers 12Event C: An even number on the second roll or the third roll (or both) 34

The probability is 1/2 that a coin will turn up heads on any given toss and the probability is 1/6 that a number cube with faces numbered 1 to 6 will turn up any particular number. What is the probability of turning up heads and a 6?1/36

Susan rolled a number cube 20 times and got the following results.Outcome Rolled 1 2 3 4 5 6Number of Rolls 4 3 3 3 2 5Fill in the table below. Round your answers to the nearest thousandth.(a) From Susan's results, compute the experimental probability of rolling a 5 or 6.(b) Assuming that the cube is fair, compute the theoretical probability of rolling a 5 or 6.(c) Assuming that the cube is fair, choose the statement below that is true:With a large number of rolls, there must be no difference between the experimental and theoretical probabilities.With a large number of rolls, there might be a difference between the experimental and theoretical probabilities, but the difference should be small.With a large number of rolls, there must be a large difference between the experimental and theoretical probabilities.