<p>For events $A$ and $B$, it is given that $\mathrm{P}\left( A \right)=\frac{11}{20}$, $\mathrm{P}\left( B \right)=\frac{2}{5}$ and $\mathrm{P}\left( A\cap B \right)=\frac{1}{4}$.</p>
<ol class="i-list"><li><div class="list-item-paragraph">Find the probability where event $A$ occurs or event $B$ occurs but not both.</div><p style="text-align: right;">[1]</p></li><li><div class="list-item-paragraph">Find the probability where event $B$ has occurred but not $A$.</div><p style="text-align: right;">[1]</p></li></ol>
<p>Find a third event $C$, it is given that $\mathrm{P}\left( C \right)=\frac{1}{2}$ and that $A$ and $C$ are independent.</p>
<ol class="i-list" start="3"><li><div class="list-item-paragraph">Find the range of values of $\mathrm{P}\left( A'\cap B'\cap C \right)$.</div><p style="text-align: right;">[3]</p></li></ol>

For events $A$ and $B$, it is given that $\mathrm{P}\left( A \right)=\frac{11}{20}$, $\mathrm{P}\left( B \right)=\frac{2}{5}$ and $\mathrm{P}\left( A\cap B \right)=\frac{1}{4}$.

Find the probability where event $A$ occurs or event $B$ occurs but not both.

Find the probability where event $B$ has occurred but not $A$.

Find a third event $C$, it is given that $\mathrm{P}\left( C \right)=\frac{1}{2}$ and that $A$ and $C$ are independent.

Find the range of values of $\mathrm{P}\left( A'\cap B'\cap C \right)$.

Probability - General

Probability

H2 Math

H1 Math

International Baccalaureate Higher Level Mathematics

IB HL Math

2018 SRJC P2 Q10(b)

(i) Find P(A or B but not both) = P(A⊕B):

Given: P(C) = 1/2, A and C are independent

We need bounds on P(B∩C) and P(A∩B∩C).

For P(B∩C): max(0, P(B)+P(C)-1) ≤ P(B∩C) ≤ min(P(B), P(C))

Maximum P(A'∩B'∩C) when P(B∩C) = 0:

Minimum P(A'∩B'∩C) when P(B∩C) = 2/5:

2018 SRJC P2 Q10(b)

2018 SRJC P2 Q10(b)

Video Solution: