Using the below information calculate the conditional probability of C given each of the age groups, or P(C/D), P (C/E), etc. Compare these probabilities and speculate as to which age groups seem more likely than others to have been (according to the legal definition at that time, 0.10% blood alcohol content) intoxicated at the time they were victims.
Blood Alcohol Level of Victim
A B C
Age 0.00% 0.01-0.09% ¡Ý 0.10%
D 0-19 142 7 6 155
E 20-39 47 8 41 96
F 40-59 29 8 77 114
G 60 over 47 7 35 89
Total 265 30 159 454
To calculate the conditional probabilities of C (intoxicated victims) given each age group, we need to divide the number of cases where C occurs in each age group by the total number of cases in that age group.
Let's calculate the probabilities one by one:
P(C/D) - Probability of being intoxicated given age group D (0-19):
Number of cases where C and D intersect: 6
Total number of cases in age group D: 155
P(C/D) = 6/155 ≈ 0.0387 or 3.87%
P(C/E) - Probability of being intoxicated given age group E (20-39):
Number of cases where C and E intersect: 41
Total number of cases in age group E: 96
P(C/E) = 41/96 ≈ 0.4271 or 42.71%
P(C/F) - Probability of being intoxicated given age group F (40-59):
Number of cases where C and F intersect: 77
Total number of cases in age group F: 114
P(C/F) = 77/114 ≈ 0.6754 or 67.54%
P(C/G) - Probability of being intoxicated given age group G (60+):
Number of cases where C and G intersect: 35
Total number of cases in age group G: 89
P(C/G) = 35/89 ≈ 0.3933 or 39.33%
Comparing these probabilities, we can speculate on which age groups seem more likely to have been intoxicated at the time they were victims:
- Age group F (40-59) has the highest conditional probability (P(C/F) ≈ 67.54%), suggesting that individuals in this age group are more likely to have been intoxicated at the time they were victims.
- Age group E (20-39) also has a relatively high conditional probability (P(C/E) ≈ 42.71%), indicating a higher likelihood of intoxication compared to other age groups.
- Age group G (60+) has a lower probability (P(C/G) ≈ 39.33%) compared to F and E but higher than age group D (0-19).
- Age group D (0-19) has the lowest conditional probability (P(C/D) ≈ 3.87%), suggesting that individuals in this age group are less likely to have been intoxicated at the time they were victims.
Remember that these probabilities are based on the given data and assumptions made about the blood alcohol level of victims within each age group.