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Probability

17 marks in our Paper 1 questions. 6 questions from 2024.

Practise this topic, marked

This topic covers probability with Venn diagrams, the language of "and", "or" and "at least", and counting how many different arrangements or codes are possible. The 6 questions here are worth 17 marks in the November 2024 Paper 1 set. Of the 17 marks, 10 are for the correct final answer, 6 for method and working and 1 for explaining.

The 2024 Diagnostic Report says candidates misread "at least" and add P(M) plus P(T) plus P(G) instead of reading the answer from the Venn diagram. They use the wrong sample space for the diagram and work out the region where all three sets overlap incorrectly. In counting questions they ignore the restrictions on a code, writing answers such as 26 times 10, or use factorials where they do not belong. Fill in the diagram region by region and keep a running total.

Where marks are lost: in our words, from Department of Basic Education, NSC 2024 Diagnostic Report, Part 1 (Book 1).

Questions

These questions are not yet checked by a teacher.

Draw a Venn diagram with three overlapping circles to show ALL the learners who write these examinations, and fill in the number in every region.
(3)Based on Nov 2024 · Paper 1 · Q11.1
Calculate the probability that a learner chosen at random writes at least TWO of the three subjects.
(2)Based on Nov 2024 · Paper 1 · Q11.2
Decide whether the events "a learner sits for Mathematics" and "a learner sits for Tourism" are independent. Support your answer with calculations.
(4)Based on Nov 2024 · Paper 1 · Q11.3
A school locker uses a 4-character lock code made from the 26 letters of the alphabet and the digits 0 to 9. Every code has the pattern: digit, letter, digit, letter. Letters and digits may be used more than once in a code. Determine how many different lock codes are possible.
(2)Based on Nov 2024 · Paper 1 · Q12.1
Work out how many different passes can be made under these conditions: • No vowel (A, E, I, O, U) may be used • The first letter cannot be M or N • Within the pass, every letter is different and every digit is different • The last digit must be even
(4)Based on Nov 2024 · Paper 1 · Q12.2
A company makes 4-character codes in the form letter | digit | letter | digit. The first digit is chosen from 1 to 9 and the last digit must be an even digit (0, 2, 4, 6 or 8). Letters may be repeated. At present only 20 of the 26 letters of the alphabet may be used, which gives 18 000 different codes. The company now allows 5 of the 6 letters that were left out to be used as well, so 25 letters are available. Calculate the percentage increase in the number of different codes.
(2)Based on Nov 2024 · Paper 1 · Q12.3

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