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

A problem of mathematics is given to three students whose chances of solving the problem are $\frac{{1}}{{3}} , \frac{{1}}{{4}}$ and $\frac{{1}}{{5}}$ respectively. The probability that the question will be solved is

A bag contains $4$ white, $5$ black and $6$ red balls. If a ball is drawn at random, then what is the probability that the drawn ball is either white or red

A coin is tossed. If it shows head, we draw a ball from a bag consisting of $3$ blue and $4$ white balls; if it shows tail we throw a die. Describe the sample space of this experiment.

There are $10$ pairs of shoes in a cupboard from which $4$ shoes are picked at random. The probability that there is at least one pair, is

Suppose that a die (with faces marked $1$ to $6$) is loaded in such a manner that for $K = 1, 2, 3…., 6$, the probability of the face marked $K$ turning up when die is tossed is proportional to $K$. The probability of the event that the outcome of a toss of the die will be an even number is equal to