Embibe Experts Solutions for Exercise 1: Andhra Pradesh Board-2020

State and prove Addition theorem on probability.

Find the probability of drawing an ace or a spade from a well shuffled pack of $52$.

The probability for a contractor to get a road contract is $\frac{2}{3}$ and to get a building contract is $\frac{5}{9}$. The probability to get at least one contract is $\frac{4}{5}$. Find the probability that he gets both the contracts.

Define conditional probability.

If $A$ and $B$ are independent events with $P\left(A\right)=0.2, P\left(B\right)=0.5$, then find $P\left(A/B\right)$.

If $A$ and $B$ are independent events with $P\left(A\right)=0.2, P\left(B\right)=0.5$, then find $P\left(B/A\right)$.

If $A$ and $B$ are independent events with $P\left(A\right)=0.2, P\left(B\right)=0.5$, then find $P\left(A\cap B\right)$.

State and prove Bayes' theorem.