## TCS Practice Simple Probability Questions

Below are three sample probability questions to practice for TCS. First is a bit moderate while the rest are very simple questions. But, simple questions shouldn't be overlooked as candidates often get mislead thinking that these are tricky and working out complex formulas rather than employing a straightforward approach.

**Question 1**

Two countries - Germany and France are participating in a hockey game. Mr. Randor Guy, the famous astrologer in Germany is able to predict the winner of each match with great success. It is rumoured that in a match between 2 teams X and Y,Rando Guy picks X with the same probability as X's chances of winning. Let's assume such rumours to be true and that in a match between Germany and France, Germany the stronger team has a probability of 7/10 of winning the game. What is the probability that Randor Guy will correctly pick the winner of the Germany - France game?

a) 0.58 b) 0.68 c) 0.82 d) 0.42

**Answer : ** a) 0.58

Solution :

Randor Guy predicts the winner in games with the same probability of winning. --> statement I

Germany has got a chance of winning the game with 7/10 probability. France has got a chance of winning the game with 3/10 probability.

Probability of Randor Guy picking the Germany correctly is 7/10 while picking France is 3/10 (as per statement I).

Probability of Randor Guy picking the winning team correctly = (Probability of Germany winning the game) AND (Probability of Randor Guy picking Germany correctly) OR (Probability of France winning the game) AND (Probability of Randor Guy picking France correctly).

**Note :** In probability related formulas generally AND translates to x and OR translates to +

Therefore, Probability of Randor Guy picking the winning team correctly = (Probability of Germany winning the game) * (Probability of Randor Guy picking Germany correctly) + (Probability of France winning the game) * (Probability of Randor Guy picking France correctly).

Probability of predicting winning team = (7/10 * 7/10) + (3/10 * 3/10)

=0.58

**Question 2**

A box has 45 chocolates of different colours 20 red, 15 white and 10 black chocolates. If a chocolate is chosen at random, what is the probability of that being white chocolate?

a) 1/2 b) 1/3 c) 2/3 d) 3/4

**Answer : ** b) 1/3

Solution :

**Note : **This is a simplest of the simple questions that you can expect on probability. This is a usual case in placement tests. You should be able to identify such simple questions amidst tough questions. At times, you could get mislead by thinking this is a tricky one.

Any of 45 chocolates could be chosen. So, totally there are 45 possibilities. Since there are only 15 white chocolates, only 15 possibilities can lead to a white chocolate. Hence P(white chocolate) = 15/45 or 1/3.

**Question 3**

In an off campus placement programme, a software company recruiter interviewed 75 prospective candidates -- 10 from Civil engineering department, 5 from Bio-chemical department and rest from computer science department. If the software company finally issued offer letter to 17 candidates, what is the probability that all the selected candidates belonged to only computer science department?

a) 60C17/ 75C17 b) 65C17/75C17 c) 70C17/75C17 d) None of these.

**Answer : ** a) 60C17/75C17

Solution :

17 out of 75 candidates selected in 75C17 ways. 17 out of 60 from computer science department can be selected in 60C17 ways.

So the required probability = Ways of selecting 17 computer science candidates / Ways of selecting 17 candidates from all departments

= 60C17 / 75C17

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