BSB123 Lecture Notes - Lecture 3: Contingency Table, Dishwasher
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Tutorial 3 Bivariate Data & Probability
Extension Activity
Question 1 AAYC
The Australian Association of Young CEOs (AAYC) is a privileged group whose membership is restricted
to those who have become CEOs before the age of 40. Members must leave the Association on reaching 50.
A recent report published by AAYC reveals that 80% of its members are 40 or over, and 65% are under 45.
Define the events A and B:
A: The member randomly chosen is at least 40 years old.
B: The member randomly chosen is under 45 years old.
Express in your own words, and calculate, the following probabilities:
(a) P(
_
A
)
(b) P(A or B)
(c) P(A and B)
(d) P(A B)
(e) P(B A)
Question 2 Dishwasher
ARIA Brisbane employs Alan, Betty and Chris to wash dishes each evening. Alan washes 40% of the
dishes and breaks only 1% of those he washes. Betty and Chris each wash 30%. Betty breaks 1% of the
dishes she washes and Chris breaks 3% of his. One night you are dining at ARIA and hear a dish fall and
break on the fall. What is the probability that Chris breaks it?
(Adapted from Intro Stats (De Veaux and Vellman 2004))
Question 3 Population Size and Dependence
Consider the following two experiments.
Experiment 1
Two balls are drawn one at a time from a bag containing 10 balls – 7 white and 3 red. Consider
each of the following cases, and calculate the probability that both balls are red, i.e., P(R1 and R2).
(R1 denotes the event that the first drawn ball is red, and R2, the event that the second drawn ball
is red.)
(i) The balls are drawn with replacement.
(ii) The balls are drawn without replacement.
Experiment 2
This experiment is very similar to 1, except now the bag contains 1000 balls – 700 white and 300
red. Consider each of the following cases, and calculate P(R1 and R2).
(i) The balls are drawn with replacement.
(ii) The balls are drawn without replacement.
Refer to the results above. Discuss under what condition(s) is R2 independent of R1?
Document Summary
The australian association of young ceos (aayc) is a privileged group whose membership is restricted to those who have become ceos before the age of 40. Members must leave the association on reaching 50. A recent report published by aayc reveals that 80% of its members are 40 or over, and 65% are under 45. A: the member randomly chosen is at least 40 years old. B: the member randomly chosen is under 45 years old. Express in your own words, and calculate, the following probabilities: Aria brisbane employs alan, betty and chris to wash dishes each evening. Alan washes 40% of the dishes and breaks only 1% of those he washes. Betty breaks 1% of the dishes she washes and chris breaks 3% of his. One night you are dining at aria and hear a dish fall and break on the fall. What is the probability that chris breaks it? (adapted from intro stats (de veaux and vellman 2004))
