Please help with all parts. Thank you so much!

Question 1.

An experiment consists of tossing a nickel, a dime, and a quarter. Of interest is the side the coin lands on. . H = heads . T = tails - Part(a) List the sample space. (Type your answer using letter combinations separated by commas. Example: HHH, TTT, ...) - Part (b) Let A be the event that there are at least two tails. Find P(A). (Enter your answer as a fraction.) W: - Part (0) Let A be the event that there are at least two tails. Let B be the event that the rst and second tosses land on heads. Are the events A and B mutually exclusive? Explain your answer. 0 Events A and B are mutually exclusive because a coin can land on heads or tails but not both at the same time. 0 Events A and B are not mutually exclusive. Some of the outcomes land on heads the rst two tosses, and some of the outcomes have at least two tails. 0 Events A and B are mutually exclusive because they have different probabilities. 0 Events A and B are mutually exclusive. Having two coins land heads up cannot occur when at least two coins must be tails. Consider the following scenario: - Let P(C) = 0.4 - Let P(D) = 0.5 - Let P(C | D) = 0.6 Find P(CAND D). Are C and D mutually exclusive? Why or why not? 0 C and D are not mutually exclusive because P(C AND D) 0. O C and D are mutually exclusive because they have different probabilities. 0 There is not enough information to determine if C and D are mutually exclusive. 0 C and D are not mutually exclusive because P(C) + P(D) 1. Are C and D independent events? Why or why not? 0 The events are not independent because P(C I D) P(C)- O The events are independent because they are mutually exclusive. 0 The events are not independent because the sum of the events is less than 1. O The events are not independent because P(C) x P(D) P(C | D)- Find P(D | C). G and H are mutually exclusive events. - P(G) = 0.5 . P(H) = 0.2 3 Part(a) Explain why the following statement MUST be false: P(H| G) = 0.3. 0 To nd conditional probability, divide P(G AND H) by P(H), which gives 0.5. P(H) = P(G) O The events are mutually exclusive, which makes P(H AND G) = 0; therefore, P(H | G) = 0. O The statement is false because P(H | G) = 0.4. O The events are mutually exclusive, which means they can be added together, and the sum is not 0.3. 3 Part (b) Find P(H OR G). E] Part (0) Are G and H independent or dependent events? Explain. O G and H are independent events because they are mutually exclusive. 0 G and H are dependent events because they are mutually exclusive. 0 G and Hare dependent events because P(G OR H) 1_ 0 There is not enough information to determine if G and H are independent or dependent events. Approximately 281,000,000 people over age five live in the United States. Of these people, 55,000,000 speak a language other than English at home. Of those who speak another language at home, 62.3 percent speak Spanish. . E = speaks English at home . E' = speaks another language at home . S = speaks Spanish at home Finish each probability statement by matching the correct answer. Part (a) P(E') = ---Select--- v Part (b) P(E) = ---Select--- v Part (c) P(S and E') = ---Select--- v Part (d) P(S | E') = ---Select