List of top Mathematics Questions on Bayes' Theorem asked in CBSE Class XII

An organisation needs to select a building construction company to make houses in cities. Three companies X, Y and Z are short-listed with the probability of their selection being \(\frac{1}{3}\), \(\frac{2}{9}\) and \(\frac{4}{9}\) respectively. It was found that there were 20%, 40% and 30% chances respectively, of delivering poor construction quality.

Based on the above information, answer the following questions :

If the building constructed was found to be strong, then what is the probability that the construction contract was given to the company X ?

An organisation needs to select a building construction company to make houses in cities. Three companies X, Y and Z are short-listed with the probability of their selection being \(\frac{1}{3}\), \(\frac{2}{9}\) and \(\frac{4}{9}\) respectively. It was found that there were 20%, 40% and 30% chances respectively, of delivering poor construction quality.

Based on the above information, answer the following questions :

If a part of the newly constructed building falls off, then what is the probability that it was due to the selection of company Y or Z ?

There are three types of vaccines $A_1$, $A_2$, $A_3$, available in the market to protect the population of the country from the spread of a certain infection. According to a survey conducted, it was found that $25\%$ of the population was given Vaccine $A_1$, $35\%$ of the population was given Vaccine $A_2$ and $40\%$ of the population was given Vaccine $A_3$. The survey also stated that the probabilities that Vaccines $A_1$, $A_2$ and $A_3$ would protect against the infection were $60\%$, $55\%$ and $50\%$ respectively. Based on the above information, answer the following questions: