Probability is the measure of the likelihood of occurrence of an event. It is a numerical value that expresses the chance that a given event will occur. It has a range from $0$ to $1$, including both limits. It can be written as a fraction, decimal or percentage. A probability of $0$ means that there is no chance of an event occurring. A probability of $1$ means that an event is certain to occur.Â
(a)
Given that the two events $A$ and $B$ are such that $\text{P}(A|B)=\frac{2}{3},\,\,\text{P}(A\cap B’\,)=\frac{1}{4}$ and $\text{P}(A\cap B)=\frac{5}{12}$,
(a)Given that the two events $A$ and $B$ are such that $\text{P}(A|B)=\frac{2}{3},\,\,\text{P}(A\cap B’\,)=\frac{1}{4}$ and $\text{P}(A\cap B)=\frac{5}{12}$,
(i)
determine if $A$ and $B$ are independent,
[1]
(i) determine if $A$ and $B$ are independent,
[1]
(ii)
find $\text{P}(A\cup B)$.
[2]
(ii) find $\text{P}(A\cup B)$.
[2]
(b)
[3]
(b) Ali and Bob take turns to shoot an arrow in an Archery training session. The probability that Ali hits the bull’s eye is $0.3$ and for Bob, it is $0.4$. Ali shoots first.
Find the probability that Ali hits the bull’s eye first.
[3]
(c)
[2]
(c) Calvin, his parents and $7$ other people are seated in a round table of $10$. Find the probability that his parents are seated together but Calvin is not seated beside either of his parents.
[2]
Share with your friends!
(a)
[3]
(a) For events $A$ and $B$, it is given that $\text{P}(B)=0.4$ and $\text{P}(\,\,A|B’\,\,)=0.15$. Find $\text{P}(\,\,A\cup B\,\,)$.
[3]
(b)
[1]
Find the probability that[1]
Find the probability that(i)
the grand prize is won and the contestant selects the correct key in the first round,
[2]
[2]
(ii)
the contestant selects the correct key in the first round given that he wins the grand prize.
[2]
[2]
[3]
Last Part
Share with your friends!
For events $A$ and $B$, it is given that $\text{P}\left( A \right)=\frac{11}{20}$, $\text{P}\left( B \right)=\frac{2}{5}$ and $\text{P}\left( A\cap B \right)=\frac{1}{4}$.
(i)
[1]
(i) Find the probability where event $A$ occurs or event $B$ occurs but not both.
[1]
(ii)
show that ${{u}_{3}}+{{u}_{4}}+{{u}_{5}}+…+{{u}_{n}}=\,p\left[ 1-{{\left( -\frac{1}{3} \right)}^{n+q}} \right]$, where the integers $p$ and $q$ are to be found.
[3]
(ii) show that ${{u}_{3}}+{{u}_{4}}+{{u}_{5}}+…+{{u}_{n}}=\,p\left[ 1-{{\left( -\frac{1}{3} \right)}^{n+q}} \right]$, where the integers $p$ and $q$ are to be found.
[3]
Share with your friends!
[Leave your answers in fraction]
The events $A$ and $B$ are such that $\text{P}\left( A|B \right)=\frac{7}{10}$, $\text{P}\left( B|A \right)=\frac{4}{15}$ and $\text{P}\left( A\cup B \right)=\frac{3}{5}$.Â
Find the exact values of
(i)
$\text{P}\left( A\cap B \right)$,
[3]
(i) $\text{P}\left( A\cap B \right)$,
[3]
(ii)
$\text{P}\left( A’\cap B \right)$.
[2]
(ii) $\text{P}\left( A’\cap B \right)$.
[2]
Find a third event $C$, it is given that $\text{P}\left( C \right)=\frac{3}{10}$ and that $A$ and $C$ are independent.
(iii)
Find $\text{P}\left( A’\cap C \right)$.
[2]
(iii) Find $\text{P}\left( A’\cap C \right)$.
[2]
(iv)
Hence state an inequality satisfied by $\text{P}\left( A’\cap B\cap C \right)$.
[1]
(iv) Hence state an inequality satisfied by $\text{P}\left( A’\cap B\cap C \right)$.
[1]
Share with your friends!
For events $A$ and $B$, it is given that $P(A\cup B)=0.8$ and $P(\left. A \right|B)=0.5$. It is also given that events $A$ and $B$ are independent.
(i)
Find $\text{P(}B\text{)}$.
(i) Find $\text{P(}B\text{)}$.
A third event $C$ is such that events $A$ and $C$ are independent and events $B$ and $C$ are independent.
(ii)
Given also that $\text{P}(C)=0.5$, find exactly the maximum and minimum possible values of $\text{P}(A\cap B\cap C)$.
[3]
Given also that $\text{P}(C)=0.5$, find exactly the maximum and minimum possible values of $\text{P}(A\cap B\cap C)$.
[3]
Share with your friends!
Download Probability Worksheet
Learn more about our H2 Math Tuition
H2 Math Question Bank
Check out our question bank, where our students have access to thousands of H2 Math questions with video and handwritten solutions.
Share with your friends!
How can we help?