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

There are 46+176 = 222 males.

There are 254+264 = 518 females.

There are a total of 740 people.

The probability of being male is 222/740 = 0.3

There are 46+254 = 300 people that bring lunch.

There are 176 + 264 = 440 people that buy lunch.

P(male | buy lunch) = 176 / 440 = 0.4

For the events to be independent, P(male) should not depend on whether the person buys lunch or not. Since the probabilities of P(male | buys lunch) = 0.4 and P(male) = 0.3 are different, buying lunch does affect the probability of whether the person is male, so the events are not independent. Answer is D.

The correct answer is:

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

Explanation:

If two events A and B are independent, then P(A|B) {read "probability of A given B} is equal to P(A).

There are 176+46 = 222 males. There are 254+264 = 518 females. This is a total of 222+518 = 740 people. This makes P(male) = 222/740 = 111/370 = 3/10.

There are 176+264 = 440 people that buy lunch. Out of these, 176 are male. This makes P(male | buy lunch) = 176/440 = 88/220 = 8/20 = 4/10. This is because we consider only those who buy their lunch, and look at the probability that someone in that group is male.

Since P(male | buy lunch) = 4/10 ≠ P(male) = 3/10, these events are not independent.

answer: x= -2y

step-by-step explanation: