I do not know how to answer this question. Would someone please help me with each of the four question below? Thank you.
Question 1. Write the sample space for the outcomes of tossing three coins using H for heads and T for tails.
Question 2. What is the probability for each of the outcomes?
Question 3. Which kind of probability are we using here? Classical or Empirical?
Question 4. How come we do not need to have three actual coins to compute the probabilities for these outcomes?
1.
HHH
HHT
HTH
THH
HTT
THT
TTH
TTT
2. Mmmmhhh?
3. How does your course define those two terms?
4. Do you think that the coins "care" if you toss them all together or one at a time?
Sure, I'd be happy to help you with each of the four questions.
Question 1: To write the sample space for the outcomes of tossing three coins using H for heads and T for tails, we need to consider all possible combinations of heads and tails. Since each coin can have two possible outcomes (heads or tails), and there are three coins, the total number of outcomes is 2 * 2 * 2 = 8. Therefore, the sample space for this experiment is as follows:
{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Question 2: To find the probability for each of the outcomes, we need to calculate the ratio of the number of favorable outcomes to the total number of possible outcomes. For example, the probability of getting heads on all three coins (HHH) is 1 out of 8 since there is only one favorable outcome out of the eight possible outcomes. Similarly, the probability of getting tails on all three coins (TTT) is also 1 out of 8. Repeat this process for all the outcomes in the sample space to find their respective probabilities.
Question 3: In this case, we are using classical probability. Classical probability, also known as theoretical or a priori probability, relies on the assumption of equally likely outcomes. Since each coin has two sides (heads or tails) and is assumed to be fair, the probability of landing on heads or tails is equal, making classical probability applicable.
Question 4: We do not need to have three actual coins to compute the probabilities for the outcomes because we are assuming that the coins are fair and unbiased. In classical probability, we are making use of the assumption of equally likely outcomes, and we can determine the probabilities based on this assumption alone. We don't need to physically toss the coins because we already know the possible outcomes and their associated probabilities based on the assumptions we've made. This is a key feature of theoretical probability, where mathematical calculations can be used to determine probabilities without the need for physical experiments.