Questions: For the random experiment, write out an equally likely sample space, and then write the indicated events in set notation. Six people live in a dorm suite. Two are to be selected to go to the campus café to pick up a pizza. Of course, no one wants to go, so the six names (Cherry, Kaye, Laraine, Jaycie, Tilda, and Nyasia) are placed in a hat. After the hat is shaken, two names are selected. (a) Tilda is selected. (b) The two names selected have the same number of letters. Write the sample space using the first letters of the people's names. Choose the correct answer. A. C K, L J, T N B. C, K, L, J, T, N C. C K, C L, C J, C T, C N, K L, K J, K T, K N, L J, L T, L N, J T, J N, T N D. C T, K T, L T, J T, T N

Solution Steps

To solve this problem, we need to determine the sample space of selecting two people from a group of six. The sample space consists of all possible pairs of people that can be selected. Then, we identify the specific events: (a) pairs that include Tilda, and (b) pairs where both names have the same number of letters.

The sample space consists of all possible pairs of two people selected from the group of six. Using combinations, we find the sample space as follows: \[ \text{Sample Space} = \{(C, K), (C, L), (C, J), (C, T), (C, N), (K, L), (K, J), (K, T), (K, N), (L, J), (L, T), (L, N), (J, T), (J, N), (T, N)\} \]

Event (a) is the set of pairs that include Tilda ('T'). From the sample space, we select pairs containing 'T': \[ \text{Event (a)} = \{(C, T), (K, T), (L, T), (J, T), (T, N)\} \]

Event (b) is the set of pairs where both names have the same number of letters. Since all names are represented by a single letter, all pairs in the sample space satisfy this condition: \[ \text{Event (b)} = \{(C, K), (C, L), (C, J), (C, T), (C, N), (K, L), (K, J), (K, T), (K, N), (L, J), (L, T), (L, N), (J, T), (J, N), (T, N)\} \]

Final Answer