$A$ bag contains $2$ white,$3$ green,and $5$ red balls. If three balls are drawn one after the other without replacement,then the probability that the last ball drawn was red is

There are four machines and it is known that exactly two of them are faulty. They are tested one by one,in a random order,until both the faulty machines are identified. The probability that only two tests are needed is:

$A$ computer program has two modules $X$ and $Y$ and errors in them occur independently. $X$ has an error with probability $0.1$ and $Y$ has an error with probability $0.3$. If an error in $X$ alone causes the program to crash with probability $0.5$, an error in $Y$ alone causes the program to crash with probability $0.7$, and an error in both $X$ and $Y$ causes the program to crash with probability $0.8$, then the probability that the program crashes is

If $A$ and $B$ are independent events of a random experiment such that $P(A \cap B)=\frac{1}{6}$ and $P(\bar{A} \cap \bar{B})=\frac{1}{3}$, then $P(A)$ is equal to (Here, $\bar{E}$ is the complement of the event $E$)

Two numbers are selected randomly from the set $S = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$ without replacement one by one. The probability that the minimum of the two numbers is divisible by $3$ or the maximum of the two numbers is divisible by $4$ is:

$A$ die is rolled three times. The probability of getting their sum equal to a prime number of the form $4n+1$ is