The events "male” and "buys lunch” are not independent because 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
The number of male students is:
Male = 46 + 176
Male = 222
The number of female students is:
Female = 254 + 264
Female = 518
The total student is:
Total = 222 + 518
Total = 740
Next, calculate the probability of selecting a male student
P(Male) = 222/740
P(Male) = 0.3
Of all the 440 that buy lunch, 176 are male,
So, we have:
P(male | buy lunch) = 176 / 440
P(male | buy lunch) = 0.4
Because
P(male | buy lunch) and P(male) are not equal.
Then, the events "male” and "buys lunch” are not independent
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