PP1 (Shorter) Quant Section 2 (Easy) Q5

<p><span style="color:#8e44ad;"><span style="font-size:20px;">Deductions from the Given Information</span></span></p> <p>The given information does not give us much to go on here. It just says that the probability both events $E$ and $F$ will occur is $0.42$. The good news is that, because we don&#39;t have much information, we can look at extreme cases. Before doing so, a quick review. If two events are independent (which, keep in mind, we don&#39;t that they are here), the probability that they both occur can be found by simply multiplying the two probabilities together. For example, if events $A$ and $B$ are independent and the probability of $A$ is $0.3$ and the probability of $B$ is $0.5$, the probability of $A$ and $B$ occurring is $(.3)(.5)=(.15)$. So now with that out of the way we can look at our extreme cases:</p> <ul> <li><strong>Extreme case 1:&nbsp;</strong>Events $E$ and $F$ are independent. The probability of $E$ is $1$ and the probability of $F$ is $0.42$.</li> <li><strong>Extreme case 2:&nbsp;</strong>Events $E$ and $F$ are independent. The probability of $E$ is $0.42$ and the probability of $F$ is $1$.</li> </ul> <p>Notice that, in both cases, we&#39;re not violating the given information. The probability that both events $E$ and $F$ will occur is $0.42$ in both cases.</p> <p><span style="color:#27ae60;"><span style="font-size:20px;">Solving the Problem</span></span></p> <p>Much of the hard work has already been done in the deductions process. In the first case,&nbsp;<strong>Quantity A</strong>&nbsp;is $1$, which is larger than&nbsp;<strong>Quantity B&#39;s</strong>&nbsp;value of $0.58$. In the second case,&nbsp;<strong>Quantity A</strong>&nbsp;is $0.42$, which is less than <b>Quantity B.</b></p> <p>Thus, the answer is&nbsp;<strong><span style="color:#27ae60;">D, It cannot be determined</span></strong>.</p>