Probability
Basic

Lecture Notes

**Probability **s an important subject in school mathematics and also a frequently tested topic in competitive math and interviews. When it comes to brain teasers, a problem related to probability is likely to involve a question about **conditional probability**. Conditional probability can easily confuse amateurs because the probability changes after a specific event has occurred—that is, the probability is conditioned on the occurrence of a certain event.

For instance, in the example given below, the initial probability of receiving an offer letter is clearly $1/3$. However, this probability will change after the HR manager eliminates one letter, marking the occurrence of a specific event.

The best way to solve such a brain teaser is not to apply complex formulas (though that is possible if you are confident in your math skills). A more effective approach is to list all possible outcomes and then count the favorable ones among them. The answer will be simply their ratio.

Examples

(4691) $\textbf{Offer Letter}$ After a whole day of interviews, a HR manager comes with three sealed envelopes. One of them contains an offer letter, and the other two contain rejection letters. You can select one of them and will be hired if you get the offer letter. After you pick one envelope, the HR manager opens one of the other two which contains a rejection letter and offers you a chance to change your mind. Should you change your selection? Explain. |

Comments

Brain teasers related to conditional probability serve as excellent examples of creating a level playing field for individuals with diverse backgrounds. The technique used to solve such problems does not necessitate a background in mathematics, making it uncertain whether a student majoring in math can solve these problems better than candidates from other disciplines.