Home / Expert Answers / Electrical Engineering / need-help-pls-i-will-thumbs-up-nbsp-1-set-theury-asd-arwems-of-predabihty-25-pts-a-topts-pa676

# (Solved): need help pls i will thumbs up  1. (Set Theury asd Arwems of Predabihty) (25 pts) (a) (Topts ...

need help pls i will thumbs up

1. (Set Theury asd Arwems of Predabihty) (25 pts) (a) (Topts) Let events $$A_{1}$$ and $$A_{2}$$ watisfy $$P\left[A_{1} \mid=1\right.$$ and $$P\left|A_{2}\right|=1$$. Show that $$P\left(A_{1} \cap A_{2} \mid=1\right.$$. Therruchums For this quetion you are not allowed to use Venn diapratms. (b) $$(S p t s)$$ Suppose that $$P\left[A_{1} \cap A_{2}\right)=1$$, Show that $P\left[A_{2}\right] \geqslant \frac{1}{2}$ Irsetracthons: You are allowed to use any tools at your disposial. (c) (Spts) Suppore that $$P\left[A_{1}\right]=P\left[A_{2}\right]=\frac{1}{2}$$, and $$A_{1}$$ and $$A_{2}$$ are independent, Find $$P\left[A_{1} \cup A_{2}\right]$$. Instructions: Show all the steps. (d) (5 pts) Here need to justify by clearly shourng your steps. In an experiment, $$A$$ and $$B$$ are independent events and we know that $$P[A \cap B]=\frac{1}{3}$$ and $$P[A]=\frac{1}{2}$$. Are $$A$$ and $$B^{\prime}$$ mutually exclusive?

We have an Answer from Expert