GATE Overflow Test Series | Probability | Test 1 | Question: 16

Question

Suppose the probability that some part of an automobile does not work during any one hour period is $0.02,$ the probability that a given engine will work for $3$ hours will be _____

• A. $0.96$
• B. $0.98$
• C. $0.94$
• D. $0.88$

Answer 1

Let the random variable $X$ denotes the number of the one hour period when the first break down occurs.
  
P(Engine works for the $3$ hours) $= P(X \geq 4)$ (No break downs in first $3$ hours)
   
$\qquad = 1 - P(X = 1) - P( X = 2)-P(X=3)$
   
Here $X$ follows geometric distribution and we get
   
$P= 1-p - p(1-p)-p(1-p)^2$

$\qquad = 1- 0.02 - 0.02\times 0.98 - 0.02\times 0.98^2 = 0.941192$

Answer 2

Another way : 

P(not work) = 0.02

P(work) = 1 – 0.02 = 0.98

P(work for 3 hours) = 0.98 * 0.98 * 0.98 ≈ 0.9411

Answer 3

probability Engine doesn’t work for 1 hour = 0.02

probability Engine work for 1 hour= 1-0.02= 0.98

P(Engine work for 3 hours) =  0.98 x 0.98 x 0.98 = 0.94

 

 I hope my answer helps you a lot