400 randomly selected people are surveyed about income and education. Results are presented below: Low Income (L)Middle Income (M)High Income (H)College Degree (C)3273120No College Degree (N)706441Based on this sample, find the probability that a randomly selected individuala. is high income, P(H)b. is a college graduate and is in the middle income bracket, P(C and M)c. is not a college graduate or is in the low income bracket, P(N or L)d. is in the high income bracket given that the individual has a college degree, P(H | C)e. has no college degree given the individual is in the middle income bracket, P(N | M)

Question
Asked Sep 20, 2019
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400 randomly selected people are surveyed about income and education. Results are presented below:

  Low Income (L) Middle Income (M) High Income (H)
College Degree (C) 32 73 120
No College Degree (N) 70 64 41


Based on this sample, find the probability that a randomly selected individual

a. is high income, P(H)
b. is a college graduate and is in the middle income bracket, P(C and M)
c. is not a college graduate or is in the low income bracket, P(N or L)
d. is in the high income bracket given that the individual has a college degree, P(H | C)
e. has no college degree given the individual is in the middle income bracket, P(N | M)

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Expert Answer

Step 1

Note:

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Step 2

Marginal values:

The following table shows the marginal distribution of the survey result.

Low income (L) Middle income (M) High income (H)
Total
College degree(C)
No College degree (N)
32
73
120
225
70
64
41
175
Total
102
137
161
400
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Low income (L) Middle income (M) High income (H) Total College degree(C) No College degree (N) 32 73 120 225 70 64 41 175 Total 102 137 161 400

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Step 3

a. Computation of probability that a randomly selected individual has high income, P(H):

Let the event H denote high income.

From the marginal table, it is observed that out of 400 observations, 161 has high income.

The ...

Probability Number of favorable cases
Total number of outcomes
161
P(H) 400
- 0.4025
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Probability Number of favorable cases Total number of outcomes 161 P(H) 400 - 0.4025

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