Conditional probability diagrams

Probability tree & bag

<p>The events $A,B,C$ are such that $\mathrm{P}(A)=a$, $\mathrm{P}(B)=b$ and $\mathrm{P}(C)=c$, where $a$,$b$,$c$ are non-zero.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Show that if events $A$ and $B$ are independent, $A'$ and $B'$ are independent.</span></div><p style="text-align: right;">[2]</p></li><li><div class="list-item-content"><span class="list-item-text">It is given that $a=0.45$, $b=0.4$ and $c=0.5$, and that $\mathrm{P}(A\cap B\cap C)=0.1$ and events $A$ and $B$ are independent and $A$ and $C$ are independent. Find the greatest and least value of $\mathrm{P}\left( \left( A\cup B \right)\cap C \right)$.</span></div><p style="text-align: right;">[4]</p></li></ol>

The events $A,B,C$ are such that $\mathrm{P}(A)=a$, $\mathrm{P}(B)=b$ and $\mathrm{P}(C)=c$, where $a$,$b$,$c$ are non-zero.

Show that if events $A$ and $B$ are independent, $A'$ and $B'$ are independent.

It is given that $a=0.45$, $b=0.4$ and $c=0.5$, and that $\mathrm{P}(A\cap B\cap C)=0.1$ and events $A$ and $B$ are independent and $A$ and $C$ are independent. Find the greatest and least value of $\mathrm{P}\left( \left( A\cup B \right)\cap C \right)$.

2019 SAJC J2 MYE P2 Q6

2019 SAJC J2 MYE P2 Q6

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