‘$X$’ speaks truth in $60\%$ and ‘$Y$’ in $50\%$ of the cases. The probability that they contradict each other narrating the same incident is

Two dice are thrown. The probability that the sum of numbers appearing is more than $10$, is

The probability that an event will fail to happen is $0.05$. The probability that the event will take place on $4$ consecutive occasions is

The number $1,\,2,\,3$ and $4$ are written separately on four slips of paper. The slips are put in a box and mixed thoroughly, A person draws two slips from the box, one after the other, without replacement. Describe the sample space for the experiment.

From the word `$POSSESSIVE$', a letter is chosen at random. The probability of it to be $S$ is

Two dice are thrown. The events $A,\, B$ and $C$ are as follows:

$A:$ getting an even number on the first die.

$B:$ getting an odd number on the first die.

$C:$ getting the sum of the numbers on the dice $\leq 5$

State true or false $:$ (give reason for your answer)

Statement : $A$ and $C$ are mutually exclusive