Question 4 {25 marks} A pilot study on Si} respondents was conducted to study a new marketing stratm in a mobile application. It is found that 24 respondents were male and 20 respondents preferred the new marketing strategy. Among the respondents who preferred the new marketing strategy, 80% of them were male. to] Find the probability that a randomly selected respondent is male and prefers the new marketing strategy. [3 marks] [b] Find the probability that a randomly selected respondent is male or prefers the new marketing strategy. {3 marks] {c} If a randomly selected respondent is female, find the probability that she prefers the new marketing strategy. [4 marks] id] Explain whether the preference in the new marketing strategy is independent of gender. {it marks] {e} It is required to have 90% confidence in estimating the population proportion of preferring the new marketing strategy with the sampling error not greater than 0.05. Determine the optimal sample size for a future study. [6 marks]