Question

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 p(buy lunch | male) = p(male) = 0.4. p(male | buys lunch) = p(male) = 0.3. p(buy lunch | male) = 0.3 and p(male) = 0.4. p(male | buys lunch) = 0.4 and p(male) = 0.3.

Explanation:

Step1: Calculate total number of people

Total number of people \(=46 + 254+176 + 264=740\)

Step2: Calculate \(P(\text{male})\)

Number of males \(=46+176 = 222\). So \(P(\text{male})=\frac{222}{740}=0.3\)

Step3: Calculate number of people who buy lunch

Number of people who buy lunch \(=176 + 264=440\)

Step4: Calculate \(P(\text{male}|\text{buys lunch})\)

Using the formula \(P(A|B)=\frac{P(A\cap B)}{P(B)}\), here \(A\) is “male” and \(B\) is “buys lunch”. \(P(\text{male}\cap\text{buys lunch})=\frac{176}{740}\), \(P(\text{buys lunch})=\frac{440}{740}\). Then \(P(\text{male}|\text{buys lunch})=\frac{176 / 740}{440 / 740}=\frac{176}{440}=0.4\)

Answer:

\(P(\text{male}|\text{buys lunch}) = 0.4\) and \(P(\text{male}) = 0.3\)