<p>A company uses two machines, \(\mathrm{A}\)  and \(\mathrm{B}\), to makes boxes. Machines \(\mathrm{A}\) makes \(60 \%\) of the boxes.</p>
<p style="text-align: center">\(80 \%\) of the boxes made by machine \(\mathrm{A}\) pass inspection.<br>\(90 \%\) of the boxes made by machine \(\mathrm{B}\) pass inspection.</p>
<p>A box is selected at random.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Find the probability that it passes inspection.<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">The company would like the probability that a box passes inspection to be \(0.87\).<br>Find the percentage of boxes that should be made by machine \(\mathrm{B}\) to achieve this.<span class="inline-marks">[4]</span></div></li></ol>

A company uses two machines, \(\mathrm{A}\)  and \(\mathrm{B}\), to makes boxes. Machines \(\mathrm{A}\) makes \(60 \%\) of the boxes.

\(80 \%\) of the boxes made by machine \(\mathrm{A}\) pass inspection.
\(90 \%\) of the boxes made by machine \(\mathrm{B}\) pass inspection.

Find the probability that it passes inspection.

The company would like the probability that a box passes inspection to be \(0.87\).
Find the percentage of boxes that should be made by machine \(\mathrm{B}\) to achieve this.

Probability of Multiple Events

International Baccalaureate Standard Level Mathematics