There are 1000 juniors in a college. Among the 1000 juniors, 400 students are ta
ID: 3325844 • Letter: T
Question
There are 1000 juniors in a college. Among the 1000 juniors, 400 students are taking STAT200, and 700 students are taking PSYC300. There are 200 students taking both courses. Let S be the event that a randomly selected student takes STAT200, and P be the event that a randomly selected student takes PSYC300. (Show all work. Just the answer, without supporting work, will receive no credit.)
(a). Provide a written description of the complement event of (S OR P).
(b). What is the probability of complement event of (S OR P)?
Explanation / Answer
Solution:
total number of students = 1000
n(S) = 400
n (P) =700
n( S and P ) = 200
( a )
so,
n ( S OR P) = n(S) + n ( P ) - n( S and P )
n ( S OR P) = 400 + 700 - 200
n ( S OR P) = 900
=> n ( S OR P)c = 1000 - 900 = 100
the complement event of (S OR P) is randomly selecting a student who takes neither CSTAT200 nor PSYC300
n ( S OR P)c = 100
( b )
the probability of complement event of (S OR P) = n ( S OR P)c / 1000 = 100 / 1000 = 0.1
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