A fair die is relled n times. What is the probability that at least 1 of the 6 values never appeast A_(4) is defined as the value i never appeared during the is times, i=1dots, 6 .
We want to calculate the probablicy of A_(1)\cup dots\cup A_(4).
P(A_(j))=((5)/(6))^(n),i=1,dots,6
P(A_(j)\cap A_(j)]-((4)/(6))^(n),i,j=1,dots,6_(1),j!=j
P(A_(1)\cap A_(j)\cap A_(k))=((3)/(6))^(n)
By Incluaise eachasion fleorem,
P(A_(1)\cup cdots\cup A_(4))=6((5)/(6))^(n)-((6)/(2))((4)/(6))^(n) ((6)/(3))((3)/(6))^(n)-((6)/(4))((2)/(6))^(n) ((6)/(5))((1)/(6))^(n)
