In a survey of 200 people, each person was asked whether he or she uses a smartphone. The results are given below.
| Uses a smartphone | Does not use a smartphone | |
|---|---|---|
| Urban | 90 | 30 |
| Rural | 50 | 30 |
One of these people is chosen at random. Match List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| (A) | Probability that the person uses a smartphone, given that the person is urban | (I) | \(\displaystyle\frac{9}{14}\) |
| (B) | Probability that the person is urban, given that the person uses a smartphone | (II) | \(\displaystyle\frac{3}{8}\) |
| (C) | Probability that the person is rural, given that the person does not use a smartphone | (III) | \(\displaystyle\frac{1}{2}\) |
| (D) | Probability that the person does not use a smartphone, given that the person is rural | (IV) | \(\displaystyle\frac{3}{4}\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(IV), (B)-(I), (C)-(III), (D)-(II)
The totals are: urban 120, rural 80, smartphone users 140, non-users 60. In each item the given condition shrinks the sample space to one row or one column of the table.
(A) Probability that the person uses a smartphone, given that the person is urban
This matches (IV) \(\frac{3}{4}\).
\( \displaystyle P = \frac{90}{120} = \frac{3}{4} \)
(B) Probability that the person is urban, given that the person uses a smartphone
This matches (I) \(\frac{9}{14}\).
\( \displaystyle P = \frac{90}{140} = \frac{9}{14} \)
(C) Probability that the person is rural, given that the person does not use a smartphone
This matches (III) \(\frac{1}{2}\).
\( \displaystyle P = \frac{30}{60} = \frac{1}{2} \)
(D) Probability that the person does not use a smartphone, given that the person is rural
This matches (II) \(\frac{3}{8}\).
\( \displaystyle P = \frac{30}{80} = \frac{3}{8} \)