# Essay On Lab/ Mathematics (Statistics)

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Probability is used to define the process of quantifying the likelihood of an event occurring. An event defines the results of an experiment. Probability is computed by dividing the number of count of an event occurring divided by the total possible outcomes.

A is the event of the episode containing sexual behavior is 338. The total number of episodes is 959. P (A) is obtained to be 0.352.

## Question (b)

C defines the event that the episode is a comedy. The total number of episodes that are in the category comedy is 195. The total number of episodes in the experiment is 959. P(C) is obtained to be 0.203.

Conditional probability is the probability that an event will occur given that a certain event has already occurred. A defines the event that the episode contains sexual behavior. M is the event that the episode is a movie. Therefore, P (A/M) is the probability that an episode contains sexual behavior given that the episode is a movie. Conditional probability is calculated by dividing the probability of the intersection by the probability event M. The events A and M are independent because the occurrence of one event say A does not affect the occurrence of event M. Thus, the conditional event is given by the probability of event A. Therefore, P (A) is equal to P (A/M) that is 0.352.

## Question (d)

The probability of the union of an event is obtained by adding the probabilities of individual events and subtracting the intersection. B is the event that the episode does not contain sexual behavior, and it is P (B) that is given by 0.648. D is the event that the episode is a drama; its probability is P (D) is given by 0.196. The probability of the intersection of event D and B is given by 0.104. Therefore, the probability of the union of event B and D is obtained to be 0.704.

## Question (e)

D is the event that the episode is a drama, the probability of event D is obtained to be 0.196. M is the event that an episode is a movie, the probability of the M occurring is given by 0.165. These two events are independent and as such the intersection of these two events is zero. The probability of the union of event D and M is calculated to be 0.361. The complement is obtained by subtracting the value obtained from one. Therefore, the complement of the intersection is 0.639.

## Question (f)

B is the event that the episode does not contain sexual behavior, and its probability is 0.648. C is the event that the episode is a comedy. P (B/C) is obtained by dividing the intersection of events B and C by the probability of event C. P (B) is 0.648 and P (C) is 0.203. The probability of the intersections of events B and C is 0.125. The conditional probability of P (B/C) is obtained to be 0.638.

## Question (g)

The probability of a comedy containing sexual behavior is 0.078, and the probability of a drama containing sexual behavior is 0.091. A drama has a higher probability of containing sexual behavior based on the probabilities computed.

## Sexual abuse

The responses that answered yes to insomnia are 76. The total number of responses on insomnia are 134. Therefore, the probability of insomnia is obtained to be 0.567.

The probability of the intersection of events yes to both insomnia and abuse is 0.493. The probability of the event yes to abuse is 0.761. Calculating the conditional probability of Insomnia given the respondent was abused it is obtained to be 0.648.

The probability of the intersection of events insomnia and not abused is given by 0.075. The probability that the respondent was not abused is 0.239. The conditional probability of insomnia given the respondent was not abused is given by 0.314. The prevalence ratio of insomnia for abused women is obtained to be 0.647. The prevalence ratio means that the percentage of abused women who experienced insomnia 64.7% is greater than the percentage of women who were abused and did not experience insomnia. The prevalence ratio indicates that there is a correlation between insomnia and abuse.

The probability of the intersection of chest pain and abuse is 0.293. The probability that the woman was abused is 0.759. The conditional probability of chest pain given the woman was abused is 0.386. The probability of the intersection of chest pain and not abused is 0.023. The probability of no abuse is calculated to be 0.241. Calculating the conditional probability of insomnia given that the woman was not abused it is obtained to be 0.095.

The prevalence ratio of chest pain for abused women is obtained to be 0.386. This means that the percentage of women who were abused and experience chest pain is 38.6%. Therefore, the prevalence ratio indicates that the correlation between sexual abuse and chest pain is not that strong.

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