Ture or false questions: Your teacher gives a true-false pop quiz with 10 questions.
Show that the number of possible outcomes for the sample space of possible sequences of 10 answers is 1024.
I got false and the number is 182 but don't think I have the right number. Some help me.
If there were 1 question, there would be two possible sequences: T or F
If there were 2 questions, there would be 4 possible sequences: TT TF FT FF
So, if there were n questions, each can be answered in 2 ways, so you have 2^n possible sequences.
Note: your question was not T/F. The quiz had T/F questions. Your job was to prove that 1024 was the correct answer.
Since the question itself said that the answer is 1024, that was good reasoning to think that 182 was wrong. :-)
To solve this problem, let's break down the sample space of possible sequences of 10 answers.
For each question, we have two possible outcomes: either the answer is true or false. Since there are 10 questions, the total number of possible outcomes is obtained by multiplying the number of outcomes for each question together.
Therefore, the total number of possible outcomes is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 2^10 = 1024.
Hence, the correct number of possible outcomes for the sample space of possible sequences of 10 answers is 1024, not 182.
To determine the number of possible outcomes for the sample space of possible sequences of 10 answers, we need to analyze each question individually.
Since each question can be answered in one of two ways (True or False), the total number of possible outcomes for a single question is 2.
To find the number of possible outcomes for 10 questions, we need to multiply the number of outcomes for each question together. Therefore, the total number of outcomes can be calculated as:
2^10 = 1024.
So, the correct number of possible outcomes for the sample space of possible sequences of 10 answers is indeed 1024, not 182.