James surveyed people at school and asked wether they bring their lunch to school or but their lunch at school more often. The results are shown below. The events male and buys lunch are not independent because

Question

Mathematics

Drew Hammond

19 January, 08:26

James surveyed people at school and asked wether they bring their lunch to school or but their lunch at school more often. The results are shown below. The events male and buys lunch are not independent because

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Answers (1)

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Moshe Barajas · Answer 1

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.