###### A-Level H2 Math

# Probability

###### 5 Essential Questions

Here is where we provide free online Revision materials for your H2 Math. We have compiled 5 essential questions from each topic for you and broken down the core concepts with video explanations. Please download the worksheet and try the questions yourself! Have fun learning with us, consider joining our tuition classes or online courses.

- Q1
- Q2
- Q3
- Q4
- Q5

**2012 SAJC P2 Q7**

(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 bullâ€™s eye is $0.3$ and for Bob, it is $0.4$. Ali shoots first.

Find the probability that Ali hits the bullâ€™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]

**Suggested Handwritten and Video Solutions**

- (a)
- (b)
- (c)

- (a)
- (b)
- (c)

**Share with your friends!**

##### 2012 RVHS P2 Q10

(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]

**Suggested Handwritten and Video Solutions**

- (a)
- (b)
- (b)(i)
- (b)(ii)
- -

**Last Part**

- (a)
- (b)
- (b)(i)
- (b)(ii)
- -

**Last Part**

**Share with your friends!**

**2018 SRJC P2 Q10 (b)**

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]

**Suggested Handwritten and Video Solutions**

- (i)
- (ii)
- (iii)

- (i)
- (ii)
- (iii)

**Share with your friends!**

**2019 JPJC P2 Q11**

**[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]

**Suggested Handwritten and Video Solutions**

- (i)
- (ii)
- (iii)
- (iv)

- (i)
- (ii)
- (iii)
- (iv)

**Share with your friends!**

**2020 ACJC P2 Q5**

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]

**Suggested Handwritten and Video Solutions**

- (i)
- (ii)

- (i)
- (ii)

**Share with your friends!**

**Download Probability Worksheet**

**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!**