Skip to content
###### A-Level H2 Math | 5 Essential Questions

# Probability

*This free online revision course is specially designed for students to revise important topics from A Level H2 Maths. The course content is presented in an easy to study format with 5 essential questions, core concepts and explanation videos for each question. Please download the worksheet and try the questions yourself! Have fun learning with us, consider joining our tuition classes or online courses.*

**2012 SAJC P2 Q7**

**Suggested Handwritten and Video Solutions**

##### 2012 RVHS P2 Q10

In the last stage of a variety game show, the contestant aims to open a treasure chest containing the grand prize. The chest can be opened only when its two locks are unlocked. Each lock requires a unique key to be unlocked.
The contestant is given up to three rounds to select the two correct keys among six different keys on a tray. For each round, he can only select one key which will be tried on both locks. The selected key of a particular round will be removed from the tray after that round.
Show that the probability that a contestant wins the grand prize in the second round is $\frac{\text{1}}{\text{15}}$.
**Suggested Handwritten and Video Solutions**

**Last Part**

Â

**2018 SRJC P2 Q10 (b)**

**Suggested Handwritten and Video Solutions**

**2019 JPJC P2 Q11**

**Suggested Handwritten and Video Solutions**

**2020 ACJC P2 Q5**

**Suggested Handwritten and Video Solutions**

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

- Q1
- Q2
- Q3
- Q4
- Q5

(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)

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]

(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)

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]

(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]

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

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

**Share with your friends!**

WhatsApp

Telegram

Facebook

(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]

(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)

In the last stage of a variety game show, the contestant aims to open a treasure chest containing the grand prize. The chest can be opened only when its two locks are unlocked. Each lock requires a unique key to be unlocked.
The contestant is given up to three rounds to select the two correct keys among six different keys on a tray. For each round, he can only select one key which will be tried on both locks. The selected key of a particular round will be removed from the tray after that round.
Show that the probability that a contestant wins the grand prize in the second round is $\frac{\text{1}}{\text{15}}$.

[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]

(i) the grand prize is won and the contestant selects the correct key in the first round,

[2]

(ii)

the contestant selects the correct key in the first round given that he wins the grand prize.

[2]

(ii) the contestant selects the correct key in the first round given that he wins the grand prize.

[2]

The variety game show runs for five days a week, over a period of $60$ weeks. Find the probability that the mean number of shows per week for which the grand prize is won in the second round is more than $0.4$.

[3]

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

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

**Last Part**

**Share with your friends!**

WhatsApp

Telegram

Facebook

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)

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

[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]

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

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

**Share with your friends!**

WhatsApp

Telegram

Facebook

**[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]

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

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

**Share with your friends!**

WhatsApp

Telegram

Facebook

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]

- (i)
- (ii)

- (i)
- (ii)

**Share with your friends!**

WhatsApp

Telegram

Facebook

**Download Probability Worksheet**

**Learn more about our H2 Math Tuition**

Play Video

**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!**

WhatsApp

Telegram

Facebook

Pure Math

Statistics