Addition rule

[XXXYYPO]

Hi guys, below are some questions I am unsure about! Appreciate if you could clarify my doubts! Thanks!


A survey is conducted with 100 students on their favourite car brands. They tabulated the collected data as follows:
Brand Percentage
Mercedes 17.5%
Toyota 35%
BMW 13%
Mazda 28%
Others x%

(i) Comment on the validity of the numerical figures shown under the Percentage column. Correct any error that you may detect.

Unsure: The numerical figures are valid (?) as long as they add up to 100%? Not sure if there are errors there. One possible error I could thought of is the percentage must be whole number? As assuming 1% represent 1 student since there are 100 students. (Not sure if this reasoning is right) Or there are no errors?


(ii) Taking into account your answer in (i), identify the value of x if the percentages shown are interpreted as the probabilities of favourite cars when a Singaporean is randomly asked.
X = 6.5% (assuming there are no errors above)

Or do I need to round up the Mercedes % to 18%? And x will be 6%.

(iii) Identify the probability that a random favourite car response is BMW or
Mercedes.
Do I use the addition rule or special additional rules? I’m not sure if the responses are mutually exclusive or not? How do I know if it possible if one student pick 2 responses?
P(Mercedes) + P(BMW) = 30.5%

 

[Ishuda]

Hi guys, below are some questions I am unsure about! Appreciate if you could clarify my doubts! Thanks!


A survey is conducted with 100 students on their favourite car brands. They tabulated the collected data as follows:
Brand Percentage
Mercedes 17.5%
Toyota 35%
BMW 13%
Mazda 28%
Others x%

(i) Comment on the validity of the numerical figures shown under the Percentage column. Correct any error that you may detect.

Unsure: The numerical figures are valid (?) as long as they add up to 100%? Not sure if there are errors there. One possible error I could thought of is the percentage must be whole number? As assuming 1% represent 1 student since there are 100 students. (Not sure if this reasoning is right) Or there are no errors?

As Denis says and you conjecture, the percentages should be whole numbers. So the 17.5% should probably be either 17% or 18%.

(ii) Taking into account your answer in (i), identify the value of x if the percentages shown are interpreted as the probabilities of favourite cars when a Singaporean is randomly asked.

X = 6.5% (assuming there are no errors above)

Or do I need to round up the Mercedes % to 18%? And x will be 6%.

Make a decision according to the rules give to you for rounding numbers in (i). Then compute your answer. If your rules say, "round up the '5' to the next larger number" or equivalent, then yes round the Mercedes % to 18% and x will be 6%

(iii) Identify the probability that a random favourite car response is BMW or
Mercedes.
Do I use the addition rule or special additional rules? I’m not sure if the responses are mutually exclusive or not? How do I know if it possible if one student pick 2 responses?
P(Mercedes) + P(BMW) = 30.5%

Since the table is for 'favorite' that implies a single choice and no overlap [choices in table are independent]. Thus the addition rule. However, should you be using the 'corrected table' rather than the one given in the problem so that the answer is 31%.

 

[XXXYYPO]

Okay! Thanks! I have one more question, relating to the last question, in general, is it right to say we determine whether the events are mutually exclusive from the nature of the questions (getting hints from the keywords) and depending on the type of variables the question used?