A single letter is selected at random from the word “$PROBABILITY$”. The probability that the selected letter is a vowel is

Two cards are drawn without replacement from a well-shuffled pack. Find the probability that one of them is an ace of heart

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.

Three letters are dictated to three persons and an envelope is addressed to each of them, the letters are inserted into the envelopes at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope.

A coin is tossed. If it shows a tail, we draw a ball from a box which contains $2$ red and $3$  black balls. If it shows head, we throw a die. Find the sample space for this experiment.

A problem in Mathematics is given to three students $A, B, C$ and their respective probability of solving the problem is $\frac{1}{2} , \frac{1}{3} $ and $\frac{1}{4}$. Probability that the problem is solved is