Question

you decide to simulate the results of flipping a coin 15 times. you assign heads a value of 0 and tails a value of 1. use the simulated results to estimate the probability of getting heads, then compare your estimation with the theoretical probability. 0 0 1 1 0 0 1 1 0 0 0 1 1 1 0 (1 point) the simulated probability is 0.467, which is less than the theoretical probability. the simulated probability is 0.533, which is more than the theoretical probability. the simulated probability is 0.533, which is less than the theoretical probability. the simulated probability is 0.500, which is equal to the theoretical probability.

Explanation:

Step1: Count the number of heads

Heads is assigned a value of 0. Count the number of 0s in the sequence 0 0 1 1 0 0 1 1 0 0 0 1 1 1 0. There are 8 zeros.

Step2: Calculate the simulated probability

The formula for probability is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the number of favorable outcomes (heads) is 8 and the total number of outcomes (coin - flips) is 15. So the simulated probability \(P_{simulated}=\frac{8}{15}\approx0.533\).

Step3: Calculate the theoretical probability

For a fair coin, the theoretical probability of getting heads \(P_{theoretical}=\frac{1}{2} = 0.5\)

Answer:

The simulated probability is \(0.533\), which is more than the theoretical probability. So the correct option is: The simulated probability is \(0.533\), which is more than the theoretical probability.