Question

A new phone, e-corp x1 has been announced and it is what you've been waiting for, all along. you decide to read the reviews before buying it. from past experiences, you've figured out that good reviews mean that the product is good 90% of the time and bad reviews mean that it is bad 70% of the time. upon glancing through the reviews section, you find out that the x1 has been reviewed 1269 times and only 127 of them were bad reviews. what is the probability that, if you order the x1, it is a bad phone?

Answer 1

According to question, 
good reviews mean that the product is good 90% of the time. 
means 90 reviews are good out of 100.
you can also say that , 10 reviews are bad out of 100.
hence, in good reviews 10% is bad .


similarly, question again says that, in bad reviews ,
70 reviews are bad out of 100,

Now, total number of reviews = 1269 
only 127 review are bad reviews , 
so, number of good reviews = 1269 - 127 = 1142 

now, probability = (% of bad reviews in good reviews × number of good reviews + % of bad reviews in bad reviews × number of bad reviews )/total number of reviews 
=( 10/100 × 1142 + 70/100 × 127)/1269 
= (114.2 + 88.9)/1269 
= 203.1/1269 
= 2031/12690 
= 0.16 

Hence, probability of bad reviews is only just 0.16 
hence, we can't say it is bad phone . Because reviews are not greater than 50% .

Answer 2

First thing to note is that this question falls under probability. However, good reviews mean that the product is good 90% of the time. And also 90 reviews are good out of 100. perhaps it is good to say 10 reviews are bad out of 100. similarly, question again says that, in bad reviews , 70 reviews are bad out of 100, Now, total number of reviews = 1269 only 127 review are bad reviews , so, number of good reviews = 1269 - 127 = 1142 The question therefore can be solved as follows: =( 10/100 × 1142 + 70/100 × 127)/1269 = (114.2 + 88.9)/1269 = 203.1/1269 = 2031/12690 = 0.16 However, the probability of bad reviews is 0.16 Because reviews are not greater than 50%, we can't say the phone is bad. hope it helps