Question

question 6 (essay worth 4 points) (experimental probability hc) a coin is flipped at the start of every game to determine if team a (heads) or team b (tails) will get the ball first. part a: find the theoretical probability of a fair coin landing on heads. (1 point) part b: flip a coin 10 times and record the frequency of each outcome. determine the experimental probability of landing on heads. please include the frequency of each outcome in your answer. (2 points) part c: compare the experimental probability to the theoretical probability. (1 point)

Explanation:

Step1: Calculate theoretical probability

For a fair - coin, there are 2 possible outcomes (heads or tails). The theoretical probability of getting heads, $P(H)$, is given by the formula $P(H)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. Since there is 1 favorable outcome (heads) out of 2 total outcomes, $P(H)=\frac{1}{2}=0.5$.

Step2: Conduct the experiment

Flip the coin 10 times. Let's assume the number of heads obtained is $n$. For example, if we flip a coin 10 times and get 4 heads and 6 tails. The experimental probability of getting heads, $P_{exp}(H)$, is calculated using the formula $P_{exp}(H)=\frac{n}{\text{Total number of flips}}$. Here, the total number of flips is 10, and if $n = 4$, then $P_{exp}(H)=\frac{4}{10}=0.4$.

Step3: Compare probabilities

The theoretical probability of getting heads is 0.5 and the experimental probability (in our example) is 0.4. In general, as the number of trials increases, the experimental probability will get closer to the theoretical probability.

Answer:

Theoretical probability of a fair - coin landing on heads: $P(H) = 0.5$. Experimental probability depends on the actual number of heads obtained in 10 flips. For example, if 4 heads are obtained in 10 flips, the experimental probability $P_{exp}(H)=0.4$.