Conditional probability sheet3-mark answer frameA pair of dice is thrown. Find the probability that the sum is 8, given that the first die shows an even number.
How to lay out the answer. Follow the frame, then write it in your own words.
- 1 · Write what is given and what is to be found. Given: two dice, 36 equally likely outcomes. To find: P(sum is 8 | first die is even).
- 2 · Name the events. Let E: the sum is 8, and F: the first die shows an even number.
- 3 · Write the formula. P(E|F) = n(E ∩ F)/n(F) = P(E ∩ F)/P(F)
- 4 · Count the outcomes.
- F: first die 2, 4 or 6 with any second die, so n(F) = 3 × 6 = 18
- E ∩ F = {(2, 6), (4, 4), (6, 2)}, so n(E ∩ F) = 3
- P(E|F) = 3/18
- 5 · Check and box the answer. 3/18 = 1/6. Check: (3, 5) and (5, 3) also give 8 but are left out, since 3 and 5 are odd. P(E|F) = 1/6.
Scoring tip: List the outcomes of E ∩ F. A correct list earns marks even if the division slips.
