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
Example 2, CJC Prelim 2016 P2, Q5ii
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
Example 2: 2014 AJC Prelim P2 Question 7iv
TJC JC2 Mar Common Test 2016
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 6th week is the second busy week, given that there is at most one busy week in the first four weeks.
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
iii Alternative solution
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.
Using TI 84 Plus (OS 2.55)
Therefore, smallest value of n =23
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.
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
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