Forty- three percent of Americans uses social media and other websites to voice

Question

Forty- three percent of Americans uses social media and other websites to voice their opinions about televisions programs (The Huffington Post, November 23, 2011). Below are the results of a survey of 1400 individuals who were asked if they use social media and other websites to voice their opinions about televisions programs. Use Social Media (SM) Don't Use Social Media (SM') Total Female 395 291 Male 323 355 Total 1.     What is the probability a respondent is a female? 2.     What is the Conditional probability a respondent uses social media and other websites to voice opinions about televisions programs given the respondent is a female? 3.     Let F denote the event that the respondent is female and SM denote the event that the respondent uses social media and other websites to voice opinions about television programs. Are events F and A independent? Forty- three percent of Americans uses social media and other websites to voice their opinions about televisions programs (The Huffington Post, November 23, 2011). Below are the results of a survey of 1400 individuals who were asked if they use social media and other websites to voice their opinions about televisions programs. Use Social Media (SM) Don't Use Social Media (SM') Total Female 395 291 Male 323 355 Total 1.     What is the probability a respondent is a female? 2.     What is the Conditional probability a respondent uses social media and other websites to voice opinions about televisions programs given the respondent is a female? 3.     Let F denote the event that the respondent is female and SM denote the event that the respondent uses social media and other websites to voice opinions about television programs. Are events F and A independent?

Explanation / Answer

1)   probability a respondent is a female P(F)=686/1364 =0.5029

2)

Conditional probability a respondent uses social media and other websites to voice opinions about televisions programs given the respondent is a female P(SM|F)=395/686 =0.5758

3) here probability  the respondent uses social media =P(SM) =395/1364 =0.2896

as from above we can see that P(SM|F) is not equal to P(SM) therefore  events F and SM are not independent

SM not SM total female 395 291 686 male 323 355 678 total 718 646 1364

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