Answer to Question #316770 in Statistics and Probability for Fiona

Question

A master’s student, Mr Nkandimeng Ledwaba’s task this semester is to contact the Research Office at the University of Limpopo for support for the university’s National Research Fund (NRF). Studies conducted in South Africa and elsewhere, point out that the probability that each of the his calls is answered is 1 3 . What will be the probability that the second call to be answered on one particular day is his sixth call?

Answer 1

From the first 5 calls only one is answered, the probability of this is $5\cdot \frac{1}{3}\cdot \left( \frac{2}{3} \right) ^4=\frac{80}{243}$

The sixth call is answered, the probability of this is 1/3.

The total probability is $\frac{80}{243}\cdot \frac{1}{3}=\frac{80}{729}$