james surveyed people at school and asked whether they bring their lunch to school or buy their lunch at…

james surveyed people at school and asked whether they bring their lunch to school or buy their lunch at school more often. the results are shown below. bring lunch: 46 males, 254 females buy lunch: 176 males, 264 females the events \male\ and \buys lunch\ are not independent because o p(buys lunch | male) = p(male) = 0.4. o p(male | buys lunch) = p(male) = 0.3. o p(buys lunch | male) = 0.3 and p(male) = 0.4. o p(male | buys lunch) = 0.4 and p(male) = 0.3.
Answer
Answer:
P(male | buys lunch) = 0.4 and P(male) = 0.3.
Explanation:
Step1: Calculate total number of people
Total = 46+254 + 176+264=740
Step2: Calculate P(male)
Number of males = 46 + 176=222, so $P(male)=\frac{222}{740}=0.3$
Step3: Calculate number of people who buy lunch
Number of people who buy lunch = 176+264 = 440
Step4: Calculate P(male | buys lunch)
$P(male | buys lunch)=\frac{176}{440}=0.4$ Two events A and B are independent if $P(A|B)=P(A)$. Here, since $P(male | buys lunch)=0.4$ and $P(male) = 0.3$, they are not equal, so the events "male" and "buys lunch" are not independent.