# Conditional probability relationship

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As a part of your proposals. You need to submit demographic information to help demonstrate that the location chosen by the management teams will be a good investment. You have collected the following data sample of 2000 customers (specifically. the person paying the bill) on age and gender. (Please note: The bins used were dictated by the proposal review committee.)

Genderv/Age> Under 18 18-24 25-45 46-65 Over 65 Total

Male 94 176 267 221 103 861

Female 123 225 384 272 135 1139

Totals 217 401 651 493 238 2000

Q 1. Using this data. fill in the joint probability table below.

AGE

Under 18 18 to 24 25 to 45 46 to 65 Over 65 TOTALS

Male

Female

Totals

Q 2. What is the probability that the person paying the bill is over 65 (regardless of gender)?

Q 3. What is the probability that the person paying the bill is male (regardless of age)?

Q 4. Given that a customer is female. what is the probability that she is in the age group 46 to 65?

Q 5. Given that a customer is under 18. what is the probability that the customer is female?

#### Solution Preview

Q 1. Dividing each given value by total number of data points (i.e., 2000), gives absolute probability of the value, e.g.,

Probability of male candidates under age 18 = number of male candidates under age 18/total number of candidates

=> P(M^18) 94/2000 = 0.047.

Similarly, probabilities for other values are estimated -- see ...

#### Solution Summary

The solution describes how to derive absolute, joint, relationship, conditional probabilities from a given joint data in tabular form and drawing answers to specific questions.