GATE ECE 2016 Set 1 | GA | Question: 6

Question

A person moving through a tuberculosis prone zone has a $50 \%$ probability of becoming infected. However, only $30 \%$ of infected people develop the disease. What percentage of people moving through a tuberculosis prone zone remains infected but does not show symptoms of disease?

• A. $15$
• B. $33$
• C. $35$
• D. $37$

Answer 1

$\text{Probability of being infected} = 0.5$

$\text{Probability of developing disease} = 0.3$

Only when a person develops disease he will show symptoms of it and whenever a disease is developed we can expect symptoms to be shown.

So, $\text{Probability of not showing symptoms} = 1-0.3 =0.7$

$\text{Probability of being infected and not showing any symptoms} = 0.5 \times 0.7 = 0.35$

Correct Answer: C $35\%$

Comments

50% probability of becoming infected

30% of 50% are infected people who developed the disease

30/100*50/100= 15%

Remaining who remains infected but don't show symptoms of disease 50%-15% = 35 %

Answer 2

Option c) 35

$P\text{(infected)} = 0.5 ,$

$P\left(\dfrac{No.of\; disease}{Infected}\right) = 0.7 \times 0.5 = 0.35$

Answer 3

Ans. A = 15%

Coz 30% of 50% will be infected. So 50% multiplied with 30% equals 15%

Answer 4

Tuberculosis

Not infect.                              infected

50%.                                            50%

                                  Devlop dis.       Does not dev

                                   30%of 50.        70%of 50%

 

70/100 *50/100. =35/100=35%

Answer 5

50% probability if a person passes through a tuberculosis zone  and only 30% of infected people shows symptoms

so 70% do not show any symptoms  percentage of people moving through a tuberculosis prone zone remains infected but does not show symptoms of disease

=50*70/100=35%