Question

Forty-three percent of Americans use social media and other websites to voice their opinions about

television programs (the Huffington Post, November 23, 2011). Below are the results of a survey of
1364 individuals who were asked if they use social media and other websites to voice their opinions
about Television programs
Uses Social Media and Other Websites to
Voice Opinions About Television Programs
Doesn’t Use Social Media and
Other Websites to Voice
Opinions About Television
Programs
Female 395 291
Male 323 355
a. Show a joint probability table. (2 marks)
b. What is the probability a respondent is female? (2 marks)
c. What is the conditional probability a respondent uses social media and other websites to voice
opinions about television programs given the respondent is female? (3 marks)
d. Let F denote the event that the respondent is female and A denote the event that the
respondent uses social media and other websites to voice opinions about television programs.
Are events F and A independent?

Answer 1

(a) 0.2896 (b) 0.5029 (c)0.5758 (d)In this case they are dependent because the gender is segregated as social media user or not as asocial media worker. the probability and variable is tied to it

Step-by-step explanation:

Solution

(a)In a survey of 1,364 people, 395 were females who used social media and 232 did not. of males 232 use social media and 355 did not

To make or develop a probability table, take each group and divide their number by their total for example female that use social media is 395 of a total of 1364

395/1364 =0.2896

The probability that a woman uses social media in the survey is 0.2896

so,

A B T

Female 0.2896 0.2133 0.5029

Male 0.2368 0.2603 0.4971

Total 0.5264 0.4736 1.00

(b) To find the probability of a surveyed person being a female, we divivde the total number of females by the whole number, shown below

686/1364 = 0.5029

(c)Conditional probability is defined using the formula which is shown below:

P(A/B) = P(A∩B)/P(B)-------(1)

Where P(A∩B) is the probability of females that use social media 0.2896 and P(B) is the total female probability which is 0.5029

Now we substitute the values in the equation 1 and calculate the probability as shown below:

P(A/B) = 0.2896/0.5029 =0.5758

the conditional probability that are surveyed person is female and uses social media is 0.5758

(d) In this case they are dependent because the gender is segregated as social media user or not as asocial media worker. the probability and variable is tied to it