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A high school senior applies for admission to two colleges A and B, and suppose that: P(admitted at A) = p1, P(rejected by B) = p2, and P(rejected by at least one, A or B) = p3.
(i) Calculate the probability that the student is admitted by at least one college.
(ii) Find the numerical value of the probability in part (i), if p1 = 0.6, p2 = 0.2, and p3 = 0.3.

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Answer:

(i) [tex]p_2(1-p_1)[/tex]

(ii) 0.08

Step-by-step explanation:

(i) The probability that he is admitted by at least one college is the complement of the probability that he is rejected by both colleges.

P(admitted by at least one college) = 1 - P(rejected by both colleges)

P(rejected by both colleges) = P(rejected by A) × P(rejected by B)

P(rejected by both colleges) = (1 - P(admitted by A)) × P(rejected by B)

[tex]P(\text{rejected by both colleges}) = (1 - p_1) \times p_2 = p_2(1-p_1)[/tex]

(ii) If [tex]p_1 = 0.6[/tex] and [tex]p_2 = 0.2[/tex], then

[tex]P(\text{rejected by both colleges}) = 0.2(1-0.6) = 0.2\times0.4 = 0.08[/tex]

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