If $A$ and $B$ are events of a random experiment such that $P(A \cup B) = \frac{4}{5}$, $P(\bar{A} \cup \bar{B}) = \frac{7}{10}$, and $P(B) = \frac{2}{5}$, then $P(A)$ equals

The probability that at least one of $A$ and $B$ occurs is $0.6$. If $A$ and $B$ occur simultaneously with probability $0.3$,then $P(A') + P(B') = $

Mr. $A$ has six children and at least one child is a girl. Then,the probability that Mr. $A$ has $3$ boys and $3$ girls is:

Two players play the following game: $A$ writes $3, 5, 6$ on three different cards; $B$ writes $8, 9, 10$ on three different cards. Both draw randomly two cards from their collections. Then,$A$ computes the product of the two numbers he/she has drawn,and $B$ computes the sum of the two numbers he/she has drawn. The player getting the larger number wins. What is the probability that $A$ wins?

Describe the sample space for the indicated experiment: $A$ die is thrown two times.

$A$ die marked $1, 2, 3$ in red and $4, 5, 6$ in green is tossed. Let $A$ be the event 'the number is even' and $B$ be the event 'the number is red'. Are $A$ and $B$ independent?