) Using the table in Exercise , 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% ¡Ý0.10%
D 0-19 142 7 6 155
E 20-39 47 8 41 96
F 40-59 29 8 77 114
G 60 or over 47 7 35 89
265 30 159 454+
a. For this table, identify any two events that are mutually exclusive.
b. For this table, identify any two events that interest.
a. Mutually exclusive events are events that cannot happen at the same time. Looking at the table, we can see that the events "Blood alcohol level of victim 0.01-0.09%" and "Blood alcohol level of victim ≥0.10%" are mutually exclusive because a victim cannot have both blood alcohol levels at the same time.
b. Two events of interest in this table can be:
1. Event D: Victim's age is 0-19.
2. Event C: Victim's blood alcohol level is ≥0.10%.
We are interested in calculating the conditional probability of event C (intoxicated) given each of the age groups.
To calculate the conditional probability of C given D (P(C/D)):
P(C/D) = Number of cases where event C and event D both occur / Number of cases where event D occurs
From the table, we have:
Number of cases where event C and event D both occur = 6
Number of cases where event D occurs = 155
P(C/D) = 6/155 ≈ 0.0387
To calculate the conditional probability of C given E (P(C/E)):
P(C/E) = Number of cases where event C and event E both occur / Number of cases where event E occurs
From the table, we have:
Number of cases where event C and event E both occur = 41
Number of cases where event E occurs = 96
P(C/E) = 41/96 ≈ 0.4271
Similarly, you can calculate the conditional probabilities for event C given the other age groups F and G.
Comparing these probabilities can help in determining which age groups are more likely to have been intoxicated at the time they were victims. In this case, the age group more likely to have been intoxicated would have higher conditional probabilities for event C.