Cards are drawn one by one without replacement from a pack of $52$ cards. The probability that $10$ cards will precede the first ace is

Three letters are to be sent to different persons and addresses on the three envelopes are also written. Without looking at the addresses, the probability that the letters go into the right envelope is equal to

Two cards are drawn from a pack of $52$ cards. What is the probability that at least one of the cards drawn is an ace

The probabilities of a student getting $I, II$ and $III$ division in an examination are respectively $\frac{1}{{10}},\,\frac{3}{5}$ and $\frac{1}{4}.$ The probability that the student fails in the examination is

A coin is tossed until a head appears or until the coin has been tossed five times. If a head does not occur on the first two tosses, then the probability that the coin will be tossed $5$ times is

A card is drawn at random from a well shuffled pack of $52$ cards. The probability of getting a two of heart or diamond is