Download Form groups of two or three and discuss the following questions

Module H1 Practical 3
Conditional Probabilities
Form groups of two or three and discuss the following questions. After discussion each
group should volunteer to present one question to the rest of the class.
1. Return again to the example discussed in Session 02, i.e. the one concerning
information about children. Here we will consider just two events, namely
A = Attending school
B = Having a birth certificate
The Venn diagram for this is the following:
School Attendance
1500
950
800
Birth
Certificate
8
(a) Represent the information above in the form of a table. The table structure is shown
overleaf Your task is to complete the table, ensuring that the row cells and column cells of
the table sum correctly to the overall marginal totals.
SADC Course in Statistics
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Module H1 Practical 3
Attends School
No
Possess a Birth
Certificate
Yes
Marginal totals
No
Yes
Marginal totals
3400
(b) Now use the information in the table above to calculate, for a child selected at random
from those surveyed, the marginal probabilities corresponding to table frequencies, i.e.
(i) Probability the child attends school = P(A) =
(ii) Probability the child does not attend school = P(Ac )=
(iii) Probability the child has a birth certificate = P(B) =
(iv) Probability the child does not have a birth certificate = P(Bc )=
(c) Calculate the answers to questions below by considering the frequencies in table above.
(i) Given the child has a birth certificate, what is the probability that the child attends
school = P(A|B) =
(ii) Given the child attends school, what is the probability that the child has a birth
certificate = P(B|A) =
Find also P(A  B) and verify that
P(A|B) * P(B) = P(A  B) = P(B|A) * P(A)
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Module H1 Practical 3
2.
Recall the Law of Total Probability
P( A)  P( A  B)  P( A  B c ) .
If B1, B2 and B3 are mutually exclusive events such that B1  B2  B3  S , where S is
the sample space, then
P( A)  P( A  B1 )  P( A  B2 )  P( A  B3 ).
A similar result applies for n mutually exclusive events which make up S.
(a) Use the definition of conditional probability to write down the Law of Total
Probability in terms of conditional probabilities.
(b) For the low-cost housing project example, calculate the probability of being
under-budget using the Law of Total Probability.
SADC Course in Statistics
Module H1 Practical 3 – Page 3