Question 4.2: Petrol Brand Preference Study Table 4.1 shows the percentage......
Petrol Brand Preference Study
Table 4.1 shows the percentage frequency table for the petrol brand most preferred by 50 motorists who live in George.
(See Excel file C4.1 – petrol brands.)
(a) What is the likelihood that a randomly selected motorist prefers Engen?
(b) What is the chance that a randomly selected motorist does not prefer Shell?
(c) What is the probability of finding a motorist who prefers either the BP, Caltex, Engen or Shell brand of petrol?
Table 4.1 Petrol brand preference – frequency counts and percentages
| Petrol brand | Count | Percentage |
| BP | 13 | 26% |
| Caltex | 9 | 18% |
| Engen | 6 | 12% |
| Shell | 22 | 44% |
| Total | 50 | 100% |
(a) Let A = event (motorist who prefers Engen petrol).
Then P(A) = \frac{6}{50} = 0.12.
Thus there is only a 12% chance of finding a motorist who prefers Engen.
(b) Let A = event (motorist who prefers Shell petrol).
Let \bar{A} = event (motorist who does not prefer Shell petrol).
Since P(A) = \frac{22}{50}=0.44, then \text P(\overline{A} )=1-\text P(A)=1-0.44=0.56.
Thus there is a 56% chance of finding a motorist who does not prefer Shell petrol. This means that more than half the motorists surveyed (56%) prefer another brand of petrol.
(c) Let A_1 = event (motorist who prefers the BP brand of petrol).
Let A_2 = event (motorist who prefers the Caltex brand of petrol).
Let A_3 = event (motorist who prefers the Engen brand of petrol).
Let A_4 = event (motorist who prefers the Shell brand of petrol).
These four events represent the collectively exhaustive set of events for the variable ‘petrol brand preferred’. It is called the sample space.
Then \text P(A_1)+\text P(A_2)+\text P(A_3)+\text P(A_4)=\frac{13}{50}+\frac{9}{50}+\frac{6}{50}+\frac{22}{50}=1.
Thus there is complete certainty that a randomly chosen motorist will prefer one of these four petrol brands.