Probability Questions

$A$ and $B$ are two independent witnesses in a case. The probability that $A$ will speak the truth is $1/3$ and the probability that $B$ will speak the truth is $3/4$. If $A$ and $B$ agree on a certain statement, then the probability that the statement is true is:

For any two events $A$ and $B$, $P(A)=P(A|B)=1/4$ and $P(B|A)=1/2$. Then which of the following is NOT correct?

A fair die is thrown six times. The probability of getting a factor of 6 exactly four times is:

Below is a figure indicating a sample space $S$ and the probability of occurrences of events $A$ and $B$. Which colored section of the portion will indicate the probability of events $B$ and $A$ occurring simultaneously?

A continuous random variable $x$ has the probability density function:$f(x)=\{\begin{array}{ll}{e}^x,& -1\le x<0\\ \frac{1}{1+x^2},& 0\le x<1\\ \text{elsewhere},& e-1-\frac{\pi }{4}\end{array}$$P(-1<x<1)$ is equal to: