Calculate end-outcome probability

6 The people living in 3 houses are classified as children ( \(C\) ), parents ( \(P\) ) or grandparents ( \(G\) ). The numbers living in each house are shown in the table below.

1. All the people in all 3 houses meet for a party. One person at the party is chosen at random. Calculate the probability of choosing a grandparent.
2. A house is chosen at random. Then a person in that house is chosen at random. Using a tree diagram, or otherwise, calculate the probability that the person chosen is a grandparent.
3. Given that the person chosen by the method in part (ii) is a grandparent, calculate the probability that there is also a parent living in the house.

7 Box \(A\) contains 5 red paper clips and 1 white paper clip. Box \(B\) contains 7 red paper clips and 2 white paper clips. One paper clip is taken at random from box \(A\) and transferred to box \(B\). One paper clip is then taken at random from box \(B\).

1. Find the probability of taking both a white paper clip from box \(A\) and a red paper clip from box \(B\).
2. Find the probability that the paper clip taken from box \(B\) is red.
3. Find the probability that the paper clip taken from box \(A\) was red, given that the paper clip taken from box \(B\) is red.
4. The random variable \(X\) denotes the number of times that a red paper clip is taken. Draw up a table to show the probability distribution of \(X\).

5 Andy can walk to work, travel by bike or travel by bus. The tree diagram shows the probabilities of any day being dry or wet and the corresponding probabilities for each of Andy's methods of travel.
\includegraphics[max width=\textwidth, alt={}, center]{7df6dcad-790d-4d0e-b1a5-3371103997d9-3_732_1141_792_500} A day is selected at random. Find the probability that

1. the weather is wet and Andy travels by bus,
2. Andy walks or travels by bike,
3. the weather is dry given that Andy walks or travels by bike.