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 $p(male)=0.3$.

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

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(\text{male})=\frac{222}{740}=0.3)

Step3: Calculate P(buys lunch | male)

Number of males who buy lunch = 176, number of males = 222. So (P(\text{buys lunch}|\text{male})=\frac{176}{222}\approx0.793)

Step4: Calculate P(male | buys lunch)

Number of people who buy lunch = 176 + 264=440. So (P(\text{male}|\text{buys lunch})=\frac{176}{440}=0.4)

Two events (A) and (B) are independent if (P(A|B)=P(A)) and (P(B|A) = P(B)). Here we check the relationship between (P(\text{male}|\text{buys lunch})) and (P(\text{male}))

Answer:

P(male | buys lunch) = 0.4 and P(male) = 0.3.