8. Five mark exercise problems - III

1. In a town of \(8000\) people, \(1300\) are over \(50\) years and \(3000\) are females. It is known that \(30\%\) of the are over \(50\) years. What is the probability that a chosen individual from the town is either a female or over \(50\) years.

 

Answer:

 

The required probability is $\frac{i}{i}$.

 

2. A coin is tossed thrice. Find the probability of getting exactly two heads or at least one tail or two consecutive heads.Answer:

 

The probability is .

 

3. If \(A\), \(B\), \(C\) are any three events such that the probability of \(B\) is twice as that of probability of \(A\) and probability of \(C\) is thrice as that of probability of \(A\) and if \(P(A \cap B) = \frac{1}{6}\), \(P(B \cap C) = \frac{1}{4}\), \(P(A \cap C) = \frac{1}{8}\), \(P(A \cup B \cup C) = \frac{9}{10}\), \(P(A \cap B \cap C) = \frac{1}{15}\), then find \(P(A)\), \(P(B)\) and \(P(C)\)?

 

Answer:

 

\(P(A) =\) $\frac{i}{i}$

 

\(P(B) =\) $\frac{i}{i}$

 

\(P(C) =\) $\frac{i}{i}$