<p>A candy shop is having a lucky draw to generate publicity. On average, $4\%$ of candy bars produced contain a lucky draw ticket each.</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">The shop owner orders $r$ candy bars on a particular day. The number of candy bars that contain a lucky draw ticket each is the random variable $D$.</div><ol class="i-list"><li data-list-item-id="item-a-i" data-list-item-path="item-a/item-a-i"><div class="list-item-paragraph">State, in the context of the question, two assumptions needed to model $D$ by a binomial distribution.<span class="inline-marks">[2]</span></div><div class="list-item-paragraph">You are now given that&nbsp;$D$ can be modelled by distribution $\mathrm{B}(r, 0.04)$.</div></li><li data-list-item-id="subitem-1783578234829-0z3dzkfz6" data-list-item-path="item-a/subitem-1783578234829-0z3dzkfz6"><div class="list-item-paragraph">Find the value of $r$ if the variance is $1.92$.<span class="inline-marks">[1]</span></div></li></ol></li></ol>
<p>The shop owner orders $k$ candy bars on another day.</p>
<ol class="abc-list" start="2"><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">The probability that there are more than $3$ lucky draw tickets among the $k$ candy bars is at least $0.34$. Determine the minimum value of $k$.<span class="inline-marks">[3]</span></div></li></ol>
<p>The lucky draw box contains five numbered vouchers. Two of the vouchers are numbered $0$, the three others are numbered $1$, $2$ and $4$ respectively. A voucher is taken one at a time, at random and without replacement, until the second voucher labelled $0$ is taken out. The random variable $A$ is the sum of the numbers on the vouchers taken.</p>
<ol class="abc-list" start="3"><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-paragraph">State the possible values that&nbsp;$A$ can take and determine the probability distribution of $A$.<span class="inline-marks">[4]</span></div></li></ol>
<p>A customer plays this lucky draw once and receives $\$A$.</p>
<ol class="abc-list" start="4"><li data-list-item-id="item-1783578470095-q8uuc1pjv" data-list-item-path="item-1783578470095-q8uuc1pjv"><div class="list-item-paragraph">Find the probability that the customer receives at least $\$5$, given that he has taken out at least $4$ vouchers.<span class="inline-marks">[2]</span></div></li></ol>

A candy shop is having a lucky draw to generate publicity. On average, $4\%$ of candy bars produced contain a lucky draw ticket each.

The shop owner orders $r$ candy bars on a particular day. The number of candy bars that contain a lucky draw ticket each is the random variable $D$.

The shop owner orders $k$ candy bars on another day.

The probability that there are more than $3$ lucky draw tickets among the $k$ candy bars is at least $0.34$. Determine the minimum value of $k$.

The lucky draw box contains five numbered vouchers. Two of the vouchers are numbered $0$, the three others are numbered $1$, $2$ and $4$ respectively. A voucher is taken one at a time, at random and without replacement, until the second voucher labelled $0$ is taken out. The random variable $A$ is the sum of the numbers on the vouchers taken.

State the possible values that $A$ can take and determine the probability distribution of $A$.

A customer plays this lucky draw once and receives $\$A$.

Find the probability that the customer receives at least $\$5$, given that he has taken out at least $4$ vouchers.

Binomial Distribution

International Baccalaureate Higher Level Mathematics

2024 ACJC P2 Q11

2024 ACJC P2 Q11