Q 1.47. - Elementary Statistics

Question

Social Networking Websites. From Wikipedia.com, we obtained the top seven major active social networking websites in the United States, excluding dating websites. Ranked according to registered users, as of April 2013, from most popular to least popular, they are Facebook (F), Twitter (T), Goggle+ (G), Habbo (H), LinkedIn (L), Bebo (B), and Tagged (A). 

(a) List the 21 possible samples (without replacement) of two social media websites that can be selected from the seven. For brevity, use the initial provided. 

(b) If a simple random sampling procedure is used to obtain two of these social media websites, what are the chances of selecting B and A? T and G?

Step-by-Step Solution

Answer

Part (a)  (F, T), (F, G), (F, H), (F, L), (F, B), (F, A), (T, G), (T, H), (T, L), (T, B), (T, A), (G, H), (G, L), (G, B), (G, A), (H, L), (H, B), (H, A), (L, B), (L, A), (B, A) 

Part (b)  0.0476 for each.

Part(a) Step 1. Given information.

The given statement is:

The top seven major active social networking websites in the United States, excluding dating websites. Ranked according to registered users, as of April 2013, from most popular to least popular, they are Facebook (F), Twitter (T), Goggle+ (G), Habbo (H), LinkedIn (L), Bebo (B), and Tagged (A).  

Part (a) Step 2. List the 21 possible samples (without replacement) of two social media websites selected from the seven.

samples are:

(F, T), (F, G), (F, H), (F, L), (F, B), (F, A), (T, G), (T, H), (T, L), (T, B), (T, A), (G, H), (G, L), (G, B), (G, A), (H, L), (H, B), (H, A), (L, B), (L, A), (B, A)

Part (b) Step 1. Find the probability of selecting (B and A) and (T and G).

Total outcomes are 21.

 The probability of selecting B and A is:

$$\begin{gathered} =\frac{1}{21} \\ =0.0476 \end{gathered}$$

 The probability of selecting T and G is:

$$\begin{gathered} =\frac{1}{21} \\ =0.0476 \end{gathered}$$