Giventhe disjoint events Q and R, P(Q)=.45, P(R)=.3 a.) Find P(Q\') b.)Find P(Q

Question

Giventhe disjoint events Q and R, P(Q)=.45, P(R)=.3 a.) Find P(Q') b.)Find P(Q or R) c.) Find P(Q and R) d.) Find P(Q' and R) e.) FindP(Q and R') so heres what i thought so far a.) p(Q')= 1-.45=.55 b.)i wasn't too sure because i think the word disjoint effects what ido i wrote p(Q U R)= P(Q) + P(R) - P(Q AND R) but i could notfigure out what the overlap/intersection of Q and R was so then ithought maybe that is incorrect therefore i stopped here so pleasehelp me out im quite confused, i find this a bit challenging

Explanation / Answer

Given the disjoint events Q and R, P(Q)=.45, P(R)=.3 a.) FindP(Q') b.) Find P(Q or R) c.) Find P(Q and R) d.) Find P(Q' and R)e.) Find P(Q and R') : a) as you stated 1-.45=.55 : b)P(Q or R)= P(Q)+P(R)=.45+.3=.75 : c)P(Q and R)=P(Q)*P(R)=.45(.3)=.135 : d)P(Q' and R)=P(Q')*P(R)=.55(.3)=.165 : e)P(Q and R')=P(Q)*P(R')=.45(.7)=.315 : disjoint simply means mutually exclusive...... which means theevents cannot occur similtaneously

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