If $A$ and $B$ are any two events, then $P(\bar A \cap B) = $
$P(\bar A)\,\,\,P(\bar B)$
$1 - P(A) - P(B)$
$P(A) + P(B) - P(A \cap B)$
$P(B) - P(A \cap B)$
Two persons $A$ and $B$ throw a (fair)die (six-faced cube with faces numbered from $1$ to $6$ ) alternately, starting with $A$. The first person to get an outcome different from the previous one by the opponent wins. The probability that $B$ wins is
$A$ and $B$ are events such that $P(A)=0.42$, $P(B)=0.48$ and $P(A$ and $B)=0.16 .$ Determine $P ($ not $A ).$
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 '
Given two independent events $A$ and $B$ such $P(A)=0.3,\,P(B)=0.6 .$ Find $P($ neither $A$or $B)$
If odds against solving a question by three students are $2 : 1 , 5:2$ and $5:3$ respectively, then probability that the question is solved only by one student is