Need to confirm an answer, Please. Q: If a tree diagram is drawn for a cinomial

Question

Need to confirm an answer, Please. Q: If a tree diagram is drawn for a cinomial experiment havingn trials, how many branches will it have. The answers I have to choose from are: - 2^n - 2n - n^2 - Need to know the value of n before the number of branchescan be determined. I believe that the answer is going to be 2n. For each"n" it will be multiplied twice. Am I correct in mythinking? Thanks Need to confirm an answer, Please. Q: If a tree diagram is drawn for a cinomial experiment havingn trials, how many branches will it have. The answers I have to choose from are: - 2^n - 2n - n^2 - Need to know the value of n before the number of branchescan be determined. I believe that the answer is going to be 2n. For each"n" it will be multiplied twice. Am I correct in mythinking? Thanks

Explanation / Answer

Let's look at a simple example: You flip a coin n times. How many possible outcomes arethere? Let n = 2. We have HH, HT, TH, TT. Thus, there are 4branches. Let n = 3. We have HHH, HHT, HTH, HTT, THH, THT, TTH,TTT. Thus, there are 8 branches. As you can see, it appears that we are looking at 2^n. Now, let's think about it logically. Every time we addanother binomial trial, at the very right of the tree, we get twonodes for every one. In essence, we are multiplying by2. Add two trials, and we multiply by 4. Add threetrials, and we multiply by 8. By induction, we can see thisis add n trials, and multiply by 2^n. Hence, your answer is2^n. Let me know if this isn't clear.

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