$A$ bag contains $n + 1$ coins. Among these coins,one coin has heads on both sides,while all other coins are fair. $A$ coin is chosen at random from the bag. If the probability of getting a head when the chosen coin is tossed is $7/12$,what is the value of $n$?

Let $a, b$ and $c$ denote the outcomes of three independent rolls of a fair tetrahedral die,whose four faces are marked $1, 2, 3, 4$. If the probability that the quadratic equation $ax^2 + bx + c = 0$ has real roots is $\frac{m}{n}$,where $\operatorname{gcd}(m, n) = 1$,then $m + n$ is equal to ..........

Three persons $P, Q$ and $R$ independently try to hit a target. If the probabilities of their hitting the target are $\frac{3}{4}, \frac{1}{2}$ and $\frac{5}{8}$ respectively,then the probability that the target is hit by $P$ or $Q$ but not by $R$,is

If $A$ and $B$ are two independent events such that $P(A) = \frac{1}{2}$ and $P(B) = \frac{1}{5}$,then which of the following is true?

$A$ six-faced die is biased such that it is twice as likely to show an even number as an odd number when thrown. If the die is thrown twice,what is the probability that the sum of the two numbers obtained is even?

If three dice are thrown at a time, then the probability of getting the sum of the numbers on them as a prime number is