Answer to Question #238668 in Statistics and Probability for Mr handsome

Question

Mboma and Masilingi race against each other in a competition. If one of them wins the race, there will
be no more race, but if the race is a draw, they run another race. They run a maximum of three races.
Each time they race, the probability that Mboma wins is 0.45 and the probability that there is a draw is
0.08.
4.1.1 Draw the tree diagram that present all possible outcomes of this competition and their
probabilities [7]
4.1.2 Calculate the probability that Masilingi wins the competition. [4]

Answer 1

Solution:

Each time they race, the probability that Masilingi wins is (1-0.45-0.08 = 0.47).

4.1.1: Tree diagram:

4.1.2:

The probability that Masilingi wins the competition$=0.47+0.08\times0.47+0.08^2\times0.47$

$=0.510608$