Question 13

(a)        At the end of full time, a football match between teams A and B was goalless. The winning team had to be decided through penalty kicks. Each team had to take five kicks.  
The probability that a kick by team A will result in a goal was 0.8 and for team B the probability was 0.3. Find, correct to three decimal places, the probability that the final scores would be:

1. 4 – 2 in favour of team B;
2. 5 – 0 in favour of team A.

(b)        Three students are to be selected from 4 boys and 5 girls to represent their school in a Mathematics Quiz.
(i)         In how many ways can the three students be selected?
(ii)        What is the probability that more boys will be selected than girls?