<p>For events \(A\) and \(B\), it is given that \(\mathrm{P}(A) = \frac{11}{20}\), \(\mathrm{P}(A \cup B) = \frac{4}{5}\) and \(\mathrm{P}(B|A) = \frac{4}{11}\).</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find</span></div><ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">\(\mathrm{P}(B)\),</span><span class="inline-marks">[3]</span></div></li><li><div class="list-item-content"><span class="list-item-text">\(\mathrm{P}(A \cap B')\).</span><span class="inline-marks">[1]</span></div></li></ol></li><li><div class="list-item-content"><span class="list-item-text">Determine if the events \(A\) and \(B'\) are mutually exclusive.</span><span class="inline-marks">[1]</span></div></li></ol>
<p>A third event \(C\) is such that \(\mathrm{P}(C) = 0.6\) and \(B\) and \(C\) are independent.</p>
<ol class="i-list" start="3"><li><div class="list-item-content"><span class="list-item-text">Find \(\mathrm{P}(B \cap C)\).</span><span class="inline-marks">[1]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the range of values of \(\mathrm{P}(A \cap B' \cap C)\).</span><span class="inline-marks">[2]</span></div></li></ol>

For events \(A\) and \(B\), it is given that \(\mathrm{P}(A) = \frac{11}{20}\), \(\mathrm{P}(A \cup B) = \frac{4}{5}\) and \(\mathrm{P}(B|A) = \frac{4}{11}\).

Determine if the events \(A\) and \(B'\) are mutually exclusive.

A third event \(C\) is such that \(\mathrm{P}(C) = 0.6\) and \(B\) and \(C\) are independent.

2025 MI P2 Q8

2025 MI P2 Q8