## Microsoft Interview Question

Senior Software Development Engineers**Country:**India

**Interview Type:**In-Person

Shouldn't it be

`(1-Y)^4 = 0.1`

?

`(1-Y)^4`

is the probability that the bus would NOT pass for 20 mins.

0.9 is the probability that the bus WOULD pass in 20 mins.

Let,

p(5) : probability of seeing no bus in 5 mins.

P(10): p(5)*p(5) = p(5)^2

similarly, p(20) = p(5)^4

also,

1-p(20) = probability of seeing bus in 20 mins

1-p(20) = 0.9 ....(given in question)

p(20)= 0.1

but, p(20) = p(5)^4

hence p(5) = p(20)^1/4

p(5) = 0.1^1/4 = 0.5623

p(seeing a bus in 5 mins) = 1- p(seeing no car in 5 mins)

p(seeing a bus in 5 mins) = 1-0.5623

p(seeing a bus in 5 mins) = 0.4377

Therefore probability of seeing a bus is 0.4377

Let the probabilty of passing of bus in the time intersection of 5 min be X.

- aasshishh April 27, 2013Then the probabilty of not passing of bus in the same 5 minute intersection is Y=1-X.

Let the bus not pass for 4 '5 min intersection', i.e, for 20 mins.

The probablity of above will be Y^4.

Then as per question,

1 - Y^4 = 0.9

Y^4 = 0.1

(1-X)^4 = 0.1

X = 0.4377