The report “TV Drama/Comedy Viewers and Health Information” (cdc.gov/healthcommunication/pdf /healthstyles_2005.pdf, retrieved April 25, 2017) describes the results of a large survey that was conducted for the Centers for Disease Control and Prevention (CDC). The sample was selected in a way that the CDC believed would result in a sample that was representative of adult Americans. 

One question on the survey asked respondents if they had learned something new about a health issue or disease from a TV show in the previous 6 months.
Data from the survey was used to estimate the following probabilities, where 

L = event that a randomly selected adult American reports learning something new about a health issue or disease from a TV show in the previous 6 months and

F = event that a randomly selected adult American is female

P(L) = 0.58 P(L ⋂ F) = 0.31

Assume that P(F) = 0.5. Are the events L and F independent events? Use probabilities to justify your answer.