Solved on Jan 18, 2024

Determine the probability a person aged 46+ prefers cash payment from the given data.
$P(\text{Cash} | \text{Age } 46+) = \frac{35}{35 + 25}$

STEP 1

Assumptions
1. The table provided shows the number of people preferring Cash or Credit Card according to their age groups.
2. We are interested in the probability of a person from the age group "46+" preferring Cash.
3. The probability is calculated as the number of people in the "46+" age group preferring Cash divided by the total number of people in the "46+" age group.

STEP 2

First, we need to find the total number of people in the "46+" age group. This is the sum of people preferring Cash and Credit Card in this age group.
$Total_{46+} = Number_{Cash, 46+} + Number_{Credit\ Card, 46+}$

STEP 3

Now, plug in the given values for the number of people preferring Cash and Credit Card in the "46+" age group to calculate the total.
$Total_{46+} = 35 + 25$

STEP 4

Calculate the total number of people in the "46+" age group.
$Total_{46+} = 35 + 25 = 60$

STEP 5

Next, we need to find the number of people in the "46+" age group who prefer Cash. This information is given directly in the table.
$Number_{Cash, 46+} = 35$

STEP 6

Now, we can calculate the probability that a person in the "46+" age group prefers Cash. The probability is the number of people preferring Cash divided by the total number of people in the "46+" age group.
$Probability_{Cash, 46+} = \frac{Number_{Cash, 46+}}{Total_{46+}}$

STEP 7

Plug in the values for the number of people preferring Cash and the total number of people in the "46+" age group to calculate the probability.
$Probability_{Cash, 46+} = \frac{35}{60}$

STEP 8

Simplify the fraction to find the probability.
$Probability_{Cash, 46+} = \frac{35}{60} = \frac{7}{12}$

STEP 9

Convert the fraction to a decimal to match the answer choices provided.
$Probability_{Cash, 46+} = \frac{7}{12} \approx 0.5833$
The probability that a person who is in the age group "46+" prefers the "Cash" payment method is approximately 0.5833.
Select one: c. 0.5833

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Determine the probability a person aged 46+ prefers cash payment from the given data.
$P(\text{Cash} | \text{Age } 46+) = \frac{35}{35 + 25}$

STEP 1

STEP 2

First, we need to find the total number of people in the "46+" age group. This is the sum of people preferring Cash and Credit Card in this age group.
$Total_{46+} = Number_{Cash, 46+} + Number_{Credit\ Card, 46+}$

STEP 3

Now, plug in the given values for the number of people preferring Cash and Credit Card in the "46+" age group to calculate the total.
$Total_{46+} = 35 + 25$

STEP 4

Calculate the total number of people in the "46+" age group.
$Total_{46+} = 35 + 25 = 60$

STEP 5

Next, we need to find the number of people in the "46+" age group who prefer Cash. This information is given directly in the table.
$Number_{Cash, 46+} = 35$

STEP 6

Now, we can calculate the probability that a person in the "46+" age group prefers Cash. The probability is the number of people preferring Cash divided by the total number of people in the "46+" age group.
$Probability_{Cash, 46+} = \frac{Number_{Cash, 46+}}{Total_{46+}}$

STEP 7

Plug in the values for the number of people preferring Cash and the total number of people in the "46+" age group to calculate the probability.
$Probability_{Cash, 46+} = \frac{35}{60}$

STEP 8

Simplify the fraction to find the probability.
$Probability_{Cash, 46+} = \frac{35}{60} = \frac{7}{12}$

STEP 9

Convert the fraction to a decimal to match the answer choices provided.
$Probability_{Cash, 46+} = \frac{7}{12} \approx 0.5833$
The probability that a person who is in the age group "46+" prefers the "Cash" payment method is approximately 0.5833.
Select one: c. 0.5833

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Determine the probability a person aged 46+ prefers cash payment from the given data.P(Cash∣Age 46+)=3535+25P(\text{Cash} | \text{Age } 46+) = \frac{35}{35 + 25}P(Cash∣Age 46+)=35+2535​

STEP 1

STEP 2

STEP 3

Now, plug in the given values for the number of people preferring Cash and Credit Card in the "46+" age group to calculate the total.Total46+=35+25Total_{46+} = 35 + 25Total46+​=35+25

STEP 4

Calculate the total number of people in the "46+" age group.Total46+=35+25=60Total_{46+} = 35 + 25 = 60Total46+​=35+25=60

STEP 5

Next, we need to find the number of people in the "46+" age group who prefer Cash. This information is given directly in the table.NumberCash,46+=35Number_{Cash, 46+} = 35NumberCash,46+​=35

STEP 6

STEP 7

Plug in the values for the number of people preferring Cash and the total number of people in the "46+" age group to calculate the probability.ProbabilityCash,46+=3560Probability_{Cash, 46+} = \frac{35}{60}ProbabilityCash,46+​=6035​

STEP 8

Simplify the fraction to find the probability.ProbabilityCash,46+=3560=712Probability_{Cash, 46+} = \frac{35}{60} = \frac{7}{12}ProbabilityCash,46+​=6035​=127​

STEP 9

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Determine the probability a person aged 46+ prefers cash payment from the given data.
$P(\text{Cash} | \text{Age } 46+) = \frac{35}{35 + 25}$

Now, plug in the given values for the number of people preferring Cash and Credit Card in the "46+" age group to calculate the total.
$Total_{46+} = 35 + 25$

Calculate the total number of people in the "46+" age group.
$Total_{46+} = 35 + 25 = 60$

Next, we need to find the number of people in the "46+" age group who prefer Cash. This information is given directly in the table.
$Number_{Cash, 46+} = 35$

Plug in the values for the number of people preferring Cash and the total number of people in the "46+" age group to calculate the probability.
$Probability_{Cash, 46+} = \frac{35}{60}$

Simplify the fraction to find the probability.
$Probability_{Cash, 46+} = \frac{35}{60} = \frac{7}{12}$