2013 SAJC P2 Q7

A teacher conducted a survey on a large number of students to determine the choice of colours for painting the school hall from \(3\) colour options of white, green and blue. Of the students surveyed, \(40\%\) were boys and \(60\%\) were girls. Of the boys, \(50\%\) chose white, \(20\%\) chose green and the rest chose blue. Of the girls, \(25\%\) chose white, \(45\%\) chose green and the rest chose blue.

Draw a probability tree diagram to illustrate the above information.[1]

1. One student is randomly selected. Find the probability that the student chose white.[1]
2. Two students are randomly selected. Find the probability that the two students are of the same gender or chose different colours (or both).[3]
3. Three girls are randomly selected. Find the probability that exactly \(1\) girl chose white, given that none of them chose blue.[3]