If $P\,({A_1} \cup {A_2}) = 1 - P(A_1^c)\,P(A_2^c)$ where $c$ stands for complement, then the events ${A_1}$ and ${A_2}$ are

If $A$ and $B$ are two events, then the probability of the event that at most one of $A, B$ occurs, is

A coin is tossed twice. If events $A$ and $B$ are defined as :$A =$ head on first toss, $B = $ head on second toss. Then the probability of $A \cup B = $

If $A$ and $B$ are two independent events, then $P\,(A + B) = $

An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on the is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cards numbered $1, 2, 3,….., 9$ is randomly picked and the number on the card is noted. The probability that the noted number is either $7$ or $8$ is

A card is drawn from a pack of $52$ cards. A gambler bets that it is a spade or an ace. What are the odds against his winning this bet