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

Hey !!

◆ Probability ◆

As given ,
In a Good review ,

10 among 100 times , the product can be bad ,

While in a bad review ,
70 among 100 times the product can be bad...

Hence ,
Probability that it's a bad phone -
[ 10(1269-127) + 70(127) ] / Total number of times

---> [ 10(1142)+70(127) ] / 1269×100

---> 20310/(1269×100)

---> 677/4230 Ans.

Hope it helps :)

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Answer 2

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% .