Question

A survey of 880 individuals asked for their favorite drink between beer and wine. Use the information in Table U to answer questions 1-4. SHOW YOUR WORK Table 1: Survey of Favorite Bev- erages Male (M) Female (F) Beer (B) Wine (W) 330 140 120 290 1) Construct a joint probability table. 2) What is the percentage of individuals that do not prefer wine? 3) Do males tend to prefer beer more than females do? Hint: You need to use conditional probabilities. 4) Are events B and M independent? Explain.

Answer 1

A joint probability table was constructed using given survey data. The percentage of individuals who don't prefer wine is 51.14%. Males tend to prefer beer more than females, and the events Beer and Male are not independent.

Step-by-step explanation:

To answer these questions, we need to start by constructing a joint probability table using the given data. We were given four groups in the survey of 880 individuals: Male Beer Drinkers (MB), Male Wine Drinkers (MW), Female Beer Drinkers (FB), and Female Wine Drinkers (FW).

We know the following: MB = 330, MW = 140, FB = 120, and FW = 290.

The joint probability table would look as follows:

Beer (B)Wine (W)TotalMale (M)330140470Female (F)120290410Total450430880

The percentage of individuals that do not prefer wine is the sum of individuals who prefer beer, divided by the total number of individuals, multiplied by 100:

(MB + FB)/Total * 100 = (330 + 120)/880 * 100 = 51.14%

To determine if males tend to prefer beer more than females, we look at the conditional probabilities. For males, it's 330/470, and for females, it's 120/410. Males show a higher ratio, therefore, males tend to prefer beer more than females do.

Last, to check if B and M are independent, we would use the formula P(B|M) = P(B). We see that 330/470 is not equal to 450/880, hence B and M are not independent events.