2013 TJC P2 Q10

In a box, there are \(12\) marbles of which \(5\) are red, \(4\) are black and \(3\) are white. \(4\) marbles are taken at random from the box, each marble being replaced before the next one is taken. Find the probability that

1. 1. at least one marble of each colour is obtained,[2]
   2. at least one marble is white.[2]

Everyday, Gerald has a choice of \(2\) routes to get to school. The probability that he gets to school without being delayed is \(\frac{43}{50}\). The probability that he chooses the first route is \(\frac{3}{5}\). If he gets to school without being delayed, the probability that the first route is chosen is \(\frac{27}{43}\). Find the probability that he gets to school without being delayed if

2. 1. he chooses the first route,[3]
   2. he chooses the second route.[3]