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
$\frac{{31}}{{56}}$
$\frac{{24}}{{56}}$
$\frac{{25}}{{56}}$
None of these
Check whether the following probabilities $P(A)$ and $P(B)$ are consistently defined $P ( A )=0.5$, $ P ( B )=0.7$, $P ( A \cap B )=0.6$
Two balls are drawn at random with replacement from a box containing $10$ black and $8$ red balls. Find the probability that both balls are red.
If ${A_1},\,{A_2},...{A_n}$ are any $n$ events, then
If $A$ and $B$ are two events, then the probability of the event that at most one of $A, B$ occurs, is
Two dice are thrown. What is the probability that the sum of the numbers appearing on the two dice is $11$, if $5$ appears on the first