A coin is tossed and a die is rolled together. Draw a tree diagram and write the sample space. List the events A: a head with an even number, and B: a tail with a number greater than 4. Are A and B mutually exclusive?

1. 1 · Write what is given and what is to be found Two actions: a coin (H, T) and a die (1 to 6). To find: S, A, B, and whether A ∩ B = ∅.
2. 2 · Draw the tree diagram Draw two branches H and T, then six branches 1 to 6 from the end of each. Read each path to get an outcome.
3. 3 · Write the sample space
   • S = {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}
   • n(S) = 2 × 6 = 12
4. 4 · List the events
   • A = {H2, H4, H6}, n(A) = 3
   • B = {T5, T6}, n(B) = 2
5. 5 · Test for mutually exclusive A ∩ B = ∅, because every outcome in A has H and every outcome in B has T.
6. 6 · Check and box the answer n(S) = 12; A = {H2, H4, H6}; B = {T5, T6}. A and B are mutually exclusive.

Scoring tip: Write the sample space inside set brackets { } and give n(S). A neat, labelled tree diagram earns marks on its own.