Many students did not consider the number of possible arrangements (permutations) in probability. The following examples illustrate the common error:

**Example 1, 2011 P2, Q9**

Examiner’s report

**Example 2, CJC Prelim 2016 P2, Q5ii**

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# Category: Probability

## Common error in Probability

## Range of probability values

## Challenging Probability Problem 7

## Challenging Probability problem 6

## Challenging Probability problem 5

## Venn diagram, Inclusion and Exclusion Principle

## Challenging Probability problem 4

## Challenging Probability problem 3

## Challenging Probability problem 2

## Challenging Probability problem 1

In 2015 alevel paper 2, finding the greatest and least possible probability values stumble many students. These examples will illustrate the methodology to solve such problems.

**Example 1: 2015 alevel P2, 9 iii**

**Solution**

**Example 2: 2014 AJC Prelim P2 Question 7iv **

**Solution**

**Part i**

**Part iv**

TJC JC2 Mar Common Test 2016

**Solution**

The owner of a restaurant counts the number of banquets received by the restaurant at the end of each week. The probability that the restaurant receives at least two banquets in a randomly chosen week is 0.3. A week is considered busy if the restaurant receives at least two wedding banquets in the week.

Calculate the probability that in a period of 6 consecutive weeks, the 6^{th} week is the second busy week, given that there is at most one busy week in the first four weeks.

Ans: 0.166

**Solution**

An unbiased die is thrown 6 times. Calculate the probabilities that the six scores obtained will

i) be 1, 2,3, 4, 5,6 in some order

ii) have a product which is an even number

iii) consists of exactly two 6’s and four odd numbers

**Solution**

iii Alternative solution

6C2: 6 slots choose 2 slots to insert the two 6s. Remaining 4 slots automatically will be for the four odd numbers.

3^4: Each odd number has 3 choices. for 4 odd numbers will be 3^4

3^4: Each odd number has 3 choices. for 4 odd numbers will be 3^4

Probability = (6C2 x 3^4) / 6^6 = 5/192

A room contains n randomly chosen people. Assume that a randomly chosen person is equally likely to have been born on any day of the 365 days in a year. Find the smallest value of n such that the people in the room were all born on different days of the year is less than 0.5.

Answer: 23

**Solution**

Using TI 84 Plus (OS 2.55)

Therefore, smallest value of n =23

**Problem**

Vegetarian club consists of 2 married couples and 8 singles. The club is to select a delegation of 4 members to participate in an overseas conference. Find the probability that the delegation contains exactly one married couple.

Answer: 8/45

**Solution**

Case 1: 1 couple + 1 of the other couple + 1 single

(2 couples choose 1 couple) X (2 choose 1 from the other couple) X (8 singles choose 1) = 32

Case 2: 1 couple and 2 singles

(2 couples choose 1 couple) X (8 singles choose 2) = 56

No restrictions = 12 C 4 = 495

Probability = (32+56) / 495 = 8/45

**Problem**

A bag contains 10 orange-flavoured, 14 strawberry-flavoured and 16 cherry-flavoured sweets which are of identical shapes and sizes. Benny selects a sweet at random from the bag. If it is not cherry-flavoured, he replaces it and selects another sweet at random. He repeats the process until he obtain a cherry-flavoured sweet. Calculate the probability that

i) the first sweet selected is strawberry-flavoured and the fourth sweet is orange-flavoured;

ii) he selects an even number of sweets

**Solution**

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