In a bag there are three tickets numbered $1, 2, 3$. $A$ ticket is drawn at random and put back,and this is done four times. The probability that the sum of the numbers is even is:

For independent events $A$ and $B$,if $P(A) = \frac{1}{2}$ and $P(A \cup B) = \frac{3}{5}$,then $P(B) =$ . . . . . . .

$A$ locker can be opened by dialing a fixed three-digit code (between $000$ and $999$). $A$ stranger who does not know the code tries to open the locker by dialing three digits at random. The probability that the stranger succeeds at the $k^{th}$ trial is

Choose a number $n$ uniformly at random from the set $\{1, 2, \ldots, 100\}$. Choose one of the first seven days of the year $2014$ at random and consider $n$ consecutive days starting from the chosen day. What is the probability that among the chosen $n$ days,the number of Sundays is different from the number of Mondays?

If $E_1, E_2, \ldots, E_n$ are independent events such that $P(E_r) = \frac{1}{1+r}$ for $r = 1, 2, \ldots, n$, then the probability that at least one of $E_1, E_2, \ldots, E_n$ happens is

Three numbers are selected at random from the set ${1, 2, 3, \dots, 8}$ without replacement. Given that the minimum of the selected numbers is $3$ and the maximum is $6$, what is the probability that the third number is $4$ or $5$?