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

Answer 1

First, find the amount of males: 46 + 176 = 222

Then, add up all the people he surveyed: 46 + 254 + 176 + 264 = 740.

Now, with those two numbers, you can find the probability of being male out of the people he surveyed: 222/740 = about 0.3

Find the amount of people that buy lunch: 176 + 246 = 422

Once you have that, then find the probability of being a male who buys lunch: 176/422 = about 0.4

As you can see, the probability of being male is a different number than the probability of being a male who buys lunch. Since the numbers are different, this makes them independent from one another.

Out of the answer choices, you can see that the only answer that aligns with the work above is option D: P(male | buys lunch) = 0.4 and P(male) = 0.3.

If you are still confused on WHY D is the answer, then maybe this will help:

-"P" stands for "Probability" and "|" stands for "and". For example, P(male | buys lunch) is the same as saying "The probability of being a male AND buying lunch").

-Independent means that they do not depend on each other. Just because you are male does not mean that you will buy lunch, and just because you buy lunch does not make you a male. Being a male and buying lunch are two completely different things that do not depend on one another.

To whoever reading this, I hope this helped! Good luck with whatever you are working on; whether it be a test, quiz, or homework. <3

Answer 2

The events "male” and "buys lunch” are not independent because of the following reason.

Given,

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

To find,

The events "male” and "buys lunch” are not independent because

Solution,

The total number of people surveyed was 46+254+176+264 = 740.

The total number of males was 46 + 176 = 222.

So...

P(male) = 222 / 740 = 3 / 10

The total number of lunch buyers was 176 + 264 = 440.

So...

P(buys lunch) = 440 / 740 = 22 / 37

The total number of males who buy lunch was 176.

So...

P(male  AND  buys lunch) = 176 / 740 = 44 / 185

Events A and B are independent if:

P(A and B) = P(A) × P(B).

Here,

P(male) × P(buys lunch) = 3/10 × 22/37 = 33 / 185

                                       ≠ 44 / 185 = P(male  AND  buys lunch)

So the events "male" and "buys lunch" are not independent.

#SPJ3