<p>Consider events \(A\) and \(B\) such that&nbsp;\(\mathrm{P}(A') = \mathrm{P}(A \cup B) = \frac{3}{4}\) and \(\mathrm{P}(B|A) = \frac{2}{3}\).</p>
<ol class="abc-list"><li data-list-item-id="item-1790057372907-hkbzs4hta" data-list-item-path="item-1790057372907-hkbzs4hta"><div class="list-item-paragraph"><p>Find \(\mathrm{P}(A \cap B)\).</p><span class="inline-marks">[3]</span></div></li><li data-list-item-id="item-1790057373682-iqvq8hljo" data-list-item-path="item-1790057373682-iqvq8hljo"><div class="list-item-paragraph"><p>Show that events \(A\) and \(B\) are independent.</p><span class="inline-marks">[3]</span></div></li></ol>

Consider events \(A\) and \(B\) such that \(\mathrm{P}(A') = \mathrm{P}(A \cup B) = \frac{3}{4}\) and \(\mathrm{P}(B|A) = \frac{2}{3}\).

<p>Show that events \(A\) and \(B\) are independent.</p>

Probability

International Baccalaureate Mathematics: Analysis and Approaches Standard Level

2025 May TZ1 P1 Q5

2025 May TZ1 P1 Q5