If the roots of each of the equations $2x^2+x-1=0$, $3x^2-10x+3=0$, and $6x^2+11x-2=0$ correspond to probabilities of three events of a random experiment, then those events are

If $A$ and $B$ are any two events,then the probability that exactly one of them occurs is

One card is drawn from each of two ordinary packs of $52$ cards. The probability that at least one of them is an ace of hearts is:

The probability of obtaining an even prime number on each die,when a pair of dice is rolled,is . . . . . . .

$A$ random experiment has five outcomes $w_1, w_2, w_3, w_4$ and $w_5$. The probabilities of the occurrence of the outcomes $w_1, w_2, w_3, w_4$ and $w_5$ are respectively $\frac{1}{6}, a, b, c$ and $\frac{1}{12}$ such that $12a + 12b - 1 = 0$. If $p(w_4) = c$ and the outcomes are equally likely for $w_2, w_3, w_4$,find the probability of the outcome $w_3$. Given the condition $12a + 12b = 1$,and assuming $a=b=c$ for the remaining outcomes,find $p(w_3)$.

Two dice are thrown. The events $A$,$B$,and $C$ are as follows:
$A$: getting an even number on the first die.
$B$: getting an odd number on the first die.
$C$: getting the sum of the numbers on the dice $\leq 5$.
State true or false: (give reason for your answer)
Statement: $A$ and $B$ are mutually exclusive.