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 head and T for tails) of the coin from the flip were recorded. Here is a summary of the data from 825 trials. Outcome: 1H 2H 3H 4H 1T 2T 3T 4T
Number of trails: 101 97 103 107 105 104 97 111

Answer The Following:
a) 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

b) 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.

c) Choose the statement that is true.
1. The smaller the number of trials, the greater the likelihood that the experimental probability will be close to the theoretical probability.

2. The larger the number of trials, the greater the likelihood that the experimental probability will be close to the theoretical probability.

3. The experimental probability will never be very close to the theoretical probability, no matter the number of trials.
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