Technical Interview Preparation

fill cup5 , pour it in cup3, cup5 left with 2quarters.
pour out cup3, pour cup5 into cup3, cup3 has 2quarters.
fill cup5, pour it in cup3 until cup3 fills
now cup5 has 4quarters.

prob of colliding is
= 1st and 2nd moving towards each other + 2nd and 3rd moving towards each other + 3rd and 1st moving towards each other
= (1/2)* (1/2) + (1/2)* (1/2) + (1/2)* (1/2) = 3/4

probability of not colliding = 1- 3/4 = 1/4

For continuous clock where hours and minutes hands move continuously then the answer is 7.5 Minutes.
3.25* 30 – 15*6 = 7.5

For discrete clock where minutes hand moves after 60 secs and hours hand moves after 12 mins then the answer is 6 minutes.

In a country in which people only want boys, every family continues to have children until they have a boy. if they have a girl, they have another child. if they have a boy, they stop. what is the proportion of boys to girls in the country?

Solution:

50:50.

probability of a boy/girl is always 2 irrespective of the number of conditions.

for the above problem we can prove it with simple probability theory.

Lets assume P(b) be the probability of having a boy. P(g) be the probability of having a girl.

Total expectation of a boy is equal to (probability of having a boy at first instance + probability of having a girl then a boy + probability of having 2 girls followd by a boy + etc… )
E(b) = 1/2 + 1/2*1/2 + 1/2*1/2*1/2 + ……
it comes down to 1 ( infinite series sum = a/1-r = 1/2/1-1/2 = 1).

E(g) = 0 + 1/2 + 1/4 + 1/8….
it comes down to 1.

It means there are equal number of girls and boys in the village.

Assume 9 is twice 5; how will you write 6 times 5 in the same system of notation

Solution:

9 is twice 5. So 5 is 4.5.
6 times 5 should be 6*4.5 = 27

One train runs from A to B at 105 miles per hour; the other runs from B to A at 85 miles per hour. How far apart were the two trains 30 minutes prior to their crossing?

Solution:

Two trains are 95 miles apart 1/2 Hr before they crossed each other

Relative Speed of the trains = 85+105 = 190MPH

One hour before they crossed, they would have been 190 miles apart.

Distance between the trains 1/2 hr before they crossed would be 190/2 = 95miles

If the probability of observing a car in 30 minutes on a highway is 0.95, what is the probability of observing a car in 10 minutes (assuming constant default probability)?

probability of not observing a car in 30 mins = probabality of not observing a car in first 10 mins * not obs in next 10 mins * not obs in last 10 mins

lets assume observing a car in 10 mins = p

probability of not observing the car in 10 mins = 1-p

probability of not observing the car in 30 mins = (1-p)^3

so (1-p)^3 = 0.05

1-p = (0.05)^1/3.
p = 1- (0.05)^1/3.
p = 1- 0.37
p = 0.63.