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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.

Respuesta :

Using conditional probability, it is found that the events are not independent because:

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

What is Conditional Probability?

Conditional probability is the probability of one event happening, considering a previous event. The formula is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which:

  • P(B|A) is the probability of event B happening, given that A happened.
  • [tex]P(A \cap B)[/tex] is the probability of both A and B happening.
  • P(A) is the probability of A happening.

If two events are independent, we have that:

[tex]P(A \cap B) = P(A)P(B)[/tex]

Hence:

[tex]P(B|A) = \frac{P(A)P(B)}{P(A)} = P(B)[/tex]

The proportion of males is given by:

P(male) = (46 + 176)/(46 + 254 + 176 + 264) = 0.3.

Hence the correct option is given by:

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

More can be learned about conditional probability at https://brainly.com/question/14398287

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