List of top Mathematics Questions on Probability asked in PSEB XII

If a die is tossed once, then the probability of getting an odd prime number is:

If \( P(A) = \frac{1}{2}, P(B) = \frac{3}{8} \) and \( P(A \cap B) = \frac{1}{5} \), then \( P(A \cup B) \) is equal to:

A problem is given to 3 students whose chances of solving it are \( \frac{1}{3} \), \( \frac{1}{5} \), and \( \frac{1}{6} \). What is the probability that:
(i) Exactly one of them solves the problem?

(ii) The problem is solved?

A laboratory blood test is 99% effective in detecting a certain disease when it is in fact present. However, the test also yields a false positive result for 0.5% of the healthy person tested. If 0.1% of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive?

If \( P(A) = \frac{1}{2}, P(B) = \frac{3}{8} \) and \( P(A \cap B) = \frac{1}{5} \), then \( P(A|B) \) is equal to:

Ram and Rahim are contesting for two vacancies in a company. Probability of selection of Ram is \( \frac{7}{9} \) and that of Rahim is \( \frac{4}{7} \). What is the probability that both will be selected?