Sarvesh K Verma Solutions for Chapter: Probability, Exercise 3: Introductory Exercise

If $A$ and $B$ are two events such that $P\left(A\right)= 0.5, P\left(B\right) = 0.6$ and $P(A \cup B) = 0.8$. Find $P\left(\frac{A}{B}\right)$?

A coin is tossed twice and four possible outcomes are assumed to be equally likely. If $\mathrm{E}$ is the event, "Both head and tail have appeared and $\mathrm{F}$ be the event, at most one tail is observed ; find $\mathrm{P}\left(\frac{\mathrm{E}}{\mathrm{F}}\right)$ and $\mathrm{P}\left(\frac{\mathrm{F}}{\mathrm{E}}\right)$.

In a class $45\%$ students read English, $30\%$ read French and $20\%$ read both English and French. One student is selected at random. Find the probability that he reads French if it is known that he reads English.

A couple has two children. Find the probability that both are boys, if it is known that the older child is a boy.

Two numbers are selected at random from the integers $1$ through $9.$If the sum is even, find the probability that both numbers are odd.