Question2. If $P(A)=0.6, P(A \cup B)=0.8$, and the events $A$ and $B$ are independent, then compute the probability of $B$
3. Consider the following summary for Gender and Preferred place to study \begin{tabular}{c|c|c|c|c} & Library & Home & Cafeteria & \\ \hline Male & 55 & 40 & 35 & \\ \hline Female & 100 & 50 & 20 & \\ \hline & & & & 300 \end{tabular} (a) If we select a student at random, what is the probability that the student is male and prefer library (b) If a student prefers to study at home, what is the probability that the student is Male (c) If $M=\{$ student is male\}, $H=\{$ student prefers to study at Home $\}$, then are $M$ and $H$ independent Explain