$X$ speaks truth in $60\%$ and $Y$ in $50\%$ of the cases. The probability that they contradict each other in narrating the same incident is

In a simultaneous throw of three coins,what is the probability of getting at least $2$ tails?

Four persons can hit a target correctly with probabilities $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}$ and $\frac{1}{5}$ respectively. If all hit at the target independently,then the probability that the target would be hit,is

When a certain biased die is rolled,a particular face occurs with probability $\frac{1}{6}-x$ and its opposite face occurs with probability $\frac{1}{6}+x$. All other faces occur with probability $\frac{1}{6}$. Note that opposite faces sum to $7$ in any die. If $0 < x < \frac{1}{6}$,and the probability of obtaining a total sum of $7$ when such a die is rolled twice is $\frac{13}{96}$,then the value of $x$ is:

The probabilities that $A$ and $B$ will die within a year are $p$ and $q$ respectively. Then,the probability that only one of them will be alive at the end of the year is

The probabilities of three students solving a question are $\frac{1}{2}, \frac{1}{4},$ and $\frac{1}{6}$ respectively. What is the probability that the question is solved?