Let $A$ and $B$ be two events such that $P\overline {(A \cup B)} = \frac{1}{6},P(A \cap B) = \frac{1}{4}$ and $P(\bar A) = \frac{1}{4},$ where $\bar A$ stands for complement of event $A$. Then events $A$ and $B$ are
Independent but not equally likely
Mutually exclusive and independent
Equally likely and mutually exclusive
Equally likely but not independent
One card is drawn at random from a well shuffled deck of $52$ cards. In which of the following cases are the events $\mathrm{E}$ and $\mathrm{F}$ independent ?
$E:$ 'the card drawn is a spade'
$F:$ 'the card drawn is an ace'
Given two independent events $A$ and $B$ such that $P(A) $ $=0.3, \,P(B)=0.6$ Find $P(A$ and $B)$.
The probabilities of occurrence of two events are respectively $0.21$ and $0.49$. The probability that both occurs simultaneously is $0.16$. Then the probability that none of the two occurs is
Two students Anil and Ashima appeared in an examination. The probability that Anil will qualify the examination is $0.05$ and that Ashima will qualify the examination is $0.10 .$ The probability that both will qualify the examination is $0.02 .$ Find the probability that Atleast one of them will not qualify the examination.
One card is drawn at random from a well shuffled deck of $52$ cards. In which of the following cases are the events $E$ and $F$ independent ?
$\mathrm{E}:$ ' the card drawn is black '
$\mathrm{F}:$ ' the card drawn is a king '