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Answer:
(1) The value of P (A) is 0.4286.
(2) The value of P (B) is 0.50.
(3) The value of P (A ∩ B) is 0.2143.
(4) The the value of P (B|A) is 0.50.
(5) The events <em>A</em> and <em>B</em> are independent.
Step-by-step explanation:
The events are defined as follows:
<em>A</em> = a student in the class has a sister
<em>B</em> = a student has a brother
The information provided is:
<em>N</em> = 210
n (A) = 90
n (B) = 105
n (A ∩ B) = 45
The probability of an event <em>E</em> is the ratio of the favorable number of outcomes to the total number of outcomes.
The conditional probability of an event <em>X</em> provided that another event <em>Y</em> has already occurred is:
If the events <em>X</em> and <em>Y</em> are independent then,
(1)
Compute the probability of event <em>A</em> as follows:
The value of P (A) is 0.4286.
(2)
Compute the probability of event <em>B</em> as follows:
The value of P (B) is 0.50.
(3)
Compute the probability of event <em>A</em> and <em>B</em> as follows:
The value of P (A ∩ B) is 0.2143.
(4)
Compute the probability of <em>B</em> given <em>A</em> as follows:
The the value of P (B|A) is 0.50.
(5)
The value of P (B|A) = 0.50 = P (B).
Thus, the events <em>A</em> and <em>B</em> are independent.