Question

laming In which of the following situations is the probability calculated empirically? Out of 1000 fans at a rock concert, 600 are male, so if a random person gets called to the stage, the probability that that person will be male is 60%. A researcher conducts a survey of college students and finds that 200 out of 500 respondents identify themselves as Democratic, so the estimated probability that a college student is Democratic is 40%. A city with 100,000 people has 30,000 Caucasians, so the probability that a random person in this city is Caucasian is 30%. An economist believes that there is a 30% chance the United States will enter a recession next year. A study done by a toy company reveals that 75 out of 100 toddlers prefer a teddy bear over an action figure, so the estimated probability of a random toddler choosing a teddy bear over an action figure is 75%.

Answer 1

The empirical probability, relative frequency, or experimental probability of an event is the ratio of the number of outcomes in which a specified event occurs to the total number of trials, not in a theoretical sample space but in an actual experiment.

So, we can the scenario probability calculated empirically if it is real and not an estimate of sample used for population generalization or a guess.

So, the statements that are empirical probability are:

• Out of 1000 fans at a rock concert, 600 are males, so if a random person gets called to the stage, the probability that the person will be male is 60% - True
• A researcher conducts a survey of college students and finds that 200 out of 500 respondents identify themselves as Democratic, so the estimated probability that a college students is Democratic is 40% - False ( based on only sample)
• A city with 100,000 people has 30,000 Caucasians, so the probability that a random person in this city is Caucasian is 30% - True
• The economist believes that there is a 30% chance the United States will enter a recession next year - False (Only belief and not mathematical true value)
• A study done by a toy company reveals that 75 out of 100 toddlers prefer a teddy bear over an action figure., so the estimated probability of a random probability of a toddler choosing a tedder bear over an action figure is 75% - False because study was observed on sample and not population.

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