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PSLE Foundation Mathematics

The masses of mangoes in kg have the distribution $\mathrm N(0.3,0.1^2)$.

Find the probability that two randomly selected mangoes weigh at least 0.5 kg in total.

Mark sells fruit boxes, each of which contain 10 randomly selected blueberries and 2 randomly selected mangoes. Let the number of unblemished blueberries in a randomly selected fruit box be $U$. On average, the probability of a blueberry being unblemished is $p$.

State a reason, in the context of the question, why $U$ might not be well-modelled by a binomial distribution.

Assume now that $U$ has the distribution $\mathrm B(10,p)$. The probability that a randomly selected fruit box contains at least 8 unblemished blueberries is 0.9.

Each fruit box is classified as grade A, B or C according to the following criteria:

Show that the probability that a randomly chosen fruit box is classified as grade C is 0.316, correct to 3 significant figures.

Hence find the probability that a randomly selected grade C fruit box contains at least 8 unblemished blueberries.

The selling prices of a grade A, grade B and grade C fruit box are $\$12$, $\$10$ and $\$6$ respectively. Find the probability that the total selling price of 5 randomly selected fruit boxes is less than $\$37$.

Mark decides to amend the criteria for grade A boxes as follows:

**Each** mango in the box weighs at least 0.3 kg **and** the box contains at least 9 unblemished blueberries.

State how the percentage of fruit boxes classified as grade A will change, and explain your answer.

Binomial Models and Assumptions

Symmetry and Properties of the Normal Distribution

Applying Probability Laws

Linear Combinations of Independent Normal Variables

Determining an Unknown Binomial Success Probability

2026 EJC P2 Q11

Probability

Discrete Random Variables (DRV)

Continuous Random Variables

<p>The events $A$ and $B$ satisfy $P(A)=\dfrac{2}{5}$, $P(B')=\dfrac{3}{4}$ and $P(B\mid A)=\dfrac{1}{4}$.</p>
<ol class="i-list"><li data-list-item-id="prob-b-item-i" data-list-item-path="prob-b-item-i"><div class="list-item-paragraph">Find $P(A'\cap B')$ and hence prove that the events $A'$ and $B'$ are independent.<span class="inline-marks">[4]</span></div></li></ol>
<p>A third event $C$ satisfies $P(C)=\dfrac{1}{2}$ and $P(A\cap B\cap C)=\dfrac{1}{20}$. It is also known that&nbsp;$B$ and $C$ are independent, while $A$ and $C$ are not independent.</p>
<ol class="i-list" start="2"><li data-list-item-id="prob-b-item-ii" data-list-item-path="prob-b-item-ii"><div class="list-item-paragraph">Find the range of possible values of $P(A'\cap B'\cap C')$.<span class="inline-marks">[5]</span></div></li></ol>

The events $A$ and $B$ satisfy $P(A)=\dfrac{2}{5}$, $P(B')=\dfrac{3}{4}$ and $P(B\mid A)=\dfrac{1}{4}$.

A third event $C$ satisfies $P(C)=\dfrac{1}{2}$ and $P(A\cap B\cap C)=\dfrac{1}{20}$. It is also known that $B$ and $C$ are independent, while $A$ and $C$ are not independent.

Independent Events

Complementary Events

Conditional Probability

Probability Bounds and Inequalities

Addition Rule for Overlapping Events

<p>For events $A$ and $B$, it is given that&nbsp;$P(A)=\dfrac{1}{4}$, $P(A\cup B)=\dfrac{5}{8}$ and $P(A\cap B')=\dfrac{1}{8}$.</p>
<ol class="i-list"><li data-list-item-id="prob-a-item-i" data-list-item-path="prob-a-item-i"><div class="list-item-paragraph">Find $P(B)$.<span class="inline-marks">[1]</span></div></li><li data-list-item-id="prob-a-item-ii" data-list-item-path="prob-a-item-ii"><div class="list-item-paragraph">Determine, with a reason, whether the events $A$ and $B$ are independent.<span class="inline-marks">[2]</span></div></li></ol>
<p>For a third event $C$, it is given that&nbsp;$P(C)=\dfrac{2}{5}$, $P(A\cap B\cap C)=\dfrac{1}{20}$, and $C$ is independent of $A$.</p>
<ol class="i-list" start="3"><li data-list-item-id="prob-a-item-iii" data-list-item-path="prob-a-item-iii"><div class="list-item-paragraph">Find $P(A'\cap C)$.<span class="inline-marks">[1]</span></div></li><li data-list-item-id="prob-a-item-iv" data-list-item-path="prob-a-item-iv"><div class="list-item-paragraph">Find the range of possible values of $P(A'\cap B'\cap C')$.<span class="inline-marks">[3]</span></div></li></ol>

For events $A$ and $B$, it is given that $P(A)=\dfrac{1}{4}$, $P(A\cup B)=\dfrac{5}{8}$ and $P(A\cap B')=\dfrac{1}{8}$.

For a third event $C$, it is given that $P(C)=\dfrac{2}{5}$, $P(A\cap B\cap C)=\dfrac{1}{20}$, and $C$ is independent of $A$.

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

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