Google is one of the top tech companies and if you want to improve your probability of working there, you really need to have solid understanding of probability and statistics. These simple probability questions are one of the best way to understand a person’s approach to real-life problems. Even the shortest of probability questions has the ability to lay bare your logical and analytical skills.
If you can solve this basic probability question on your own you have the logical ability to get into Google and the rest depends on you acquiring technical and social skills.
Google’s Simple Probability Question
The probability of spotting a truck on a highway in an hour is 0.999. What is the probability of spotting a truck on that highway in 20 minutes?
You can assume a constant default probability.
Note: Spotting a truck means ‘spotting at least one truck’.
The Solution
The probability of not spotting a truck in an hour = 1 – 0.999 = 0.001
Let us say, the probability of spotting a truck in 20 minutes = p
So, the probability of not spotting a truck in 20 minutes = 1- p
Since it has a constant default probability,
The probability of not spotting a truck in the next 20 minutes = 1- p
The probability of not spotting a truck in the last 20 minutes of an hour = 1 – p
The probability of not spotting a truck in one hour = (1 – p)^{3}
This is something we know so we get our equation,
(1-p)^{3} = 0.001
1-p = 0.1
p = 0.9
The probability of spotting a truck in 20 minutes on that highway is 90%.
So, why does Google ask such simple probability questions in an interview?
When you attempt a question like this even though when your approach is correct, you can get stuck, may be with a difficult polynomial equation. The interviewer is looking at your ability to reconsider your approach and arrive at a solution. This ability comes with practice.
If you take a straightforward approach this is what the possible combinations are. You can treat it as 3 coin flips, with heads and tails being the probabilities of spotting a truck.
p is the probability of spotting a truck in 20 minutes and these are the probabilities of spotting a truck in 60 minutes which is spotting a truck in at least one ’20 minutes’ time frame.
0-20 | 20-40 |
40-60 |
p | p |
p |
p |
p |
1-p |
p |
1-p |
1-p |
p |
1-p |
p |
1-p |
p |
p |
1-p |
p |
1-p |
1-p |
1-p |
p |
So, how did we get the answer so easily? Instead of focusing on what the question asked or provided directly, we consider the probability of not spotting a truck in 60 minutes.
0-20 |
20-40 |
40-60 |
1-p | 1-p |
1-p |
Instead of solving for p, solve for 1-p and you get the answer in one step, may be within a minute.
Here are the probabilities if you substitute the answer i.e. p=0.9
0-20 |
20-40 | 40-60 |
P |
p | p | p |
0.729 |
p |
p | 1-p |
0.081 |
p |
1-p | 1-p |
0.009 |
p |
1-p | p |
0.081 |
1-p |
p | p |
0.081 |
1-p |
p | 1-p |
0.009 |
1-p |
1-p | p |
0.009 |
0.999 |
Some more basic probability questions
What is the probability of getting a sum of 9 from the two throws of a dice?
3 coins are tossed. They are unbiased. What is the probability of getting at most two heads?
4 dice are thrown simultaneously. Find the probability that all of them show the same face.
Try another ‘Google Interview Question’
Here is another Google interview question which will surely make you scratch your head. This puzzle leans more on the tricky side. Try solving this Google interview question.