- The table below gives partial data for 84 dogs cross-classified according to personality trait and breed. The cell counts for the Doberman and Retriever are missing, but row and column totals are given.
- If one dog is randomly chosen from the 84, what is the chance that it is:
i. Meek? 22/84 = 11/42 = 26.19%
ii. An aggressive Rottweiler? 3/84 = 1/28 = 3.57%
iii. Reactive or a Rottweiler? 60/84 = 5/7 = 71.43%
iv. Neither aggressive nor a Rottweiler? 22/84 = 11/42 = 26.19%
v. Meek if it is known that it is a Rottweiler? 2/84 = 1/42 = 2.38%
vi. A Rottweiler if it is known to be aggressive? 3/84 = 1/28 = 3.57%
- What value of x in the table makes the following two events independent? D = dog is a Doberman A = dog is Aggressive
Support your answer with clear probability statements involving D and A.
For the two events to be independent D and A, we must have P (A/D) = P (A)
so… x/35 = 12/84
x = 12/84 * 35
x = 5