Conditional probability in tables, trees and Venn diagrams
3 exam-style questions. Answers and the mark for each step are on the last page.
- Question 1
(a) A theatre sells 48 tickets. Of these, 18 are child tickets. Twelve of the child tickets and 21 of the adult tickets are for the evening performance. One of the evening tickets is selected at random. Work out the probability that it is a child ticket. Give a fraction in its simplest form.
- Question 2
(a) Box A contains 2 green and 3 white counters. Box B contains 4 green and 1 white counter. One counter is transferred at random from A to B. A counter is then taken at random from B and is found to be green. Work out the probability that the transferred counter was white. Give a fraction in its simplest form.
- Question 3
(a) Three sensors A, B and C work independently. The probabilities that A and B work are 0.8 and 0.6 respectively. An alarm operates if at least two sensors work. The probability that the alarm operates is 0.7. Given that the alarm operates, work out the probability that all three sensors work. Give a fraction in its simplest form. You must show your working.
Answers and marks
Question 1
(a) 4/11
- P1 Establishing or an equivalent valid method.
- P1 Establishing or an equivalent valid method.
- A1 Correct answer: 4/11
Question 2
(a) 6/11
- P1 Establishing or an equivalent valid method.
- P1 Establishing or an equivalent valid method.
- P1 Establishing or an equivalent valid method.
- A1 Correct answer: 6/11
Question 3
(a) 12/35
- P1 Establishing or an equivalent valid method.
- P1 Establishing or an equivalent valid method.
- A1 Correct answer: 12/35