2024 VJC H1 Q9

In a probability experiment, three containers have the following contents:

• A jar contains \(2\) white cards and \(5\) black cards.
• A white box contains \(4\) red balls and \(3\) blue balls.
• A black box contains \(2\) red balls and \(4\) blue balls.

One card is taken at random from the jar. If the card is white, two balls are taken from the white box, at random and without replacement. If the card is black, two balls are taken from the black box, at random and without replacement.

1. Draw a tree diagram to represent this information.[2]

Events \(W\) and \(M\) are defined as follows:

• Event \(W\): A white card is taken from the jar,
• Event \(M\): One red and one blue ball are obtained.

2. Show that \(\mathrm{P}(M) = \frac{80}{147}\).[1]
3. Find \(\mathrm{P}(W|M')\).[2]

All the cards and balls are now placed in a single container. Four objects are taken at random, one by one and with replacement, from the container.

4. Find the probability that one object of each colour is obtained.[2]