A dice marked with digit $\{1, 2, 2, 3, 3, 3\} ,$ thrown three times, then the probability of getting sum of number on face of dice is six, is equal to :-

A fair dice is thrown up to $20$ times. The probability that on the $10^{th}$ throw, the fourth six apears is :-

A man draws a card from a pack of $52$ playing cards, replaces it and shuffles the pack. He continues this processes until he gets a card of spade. The probability that he will fail the first two times is

Among $15$ players, $8$ are batsmen and $7$ are bowlers. Find the probability that a team is chosen of $6$ batsmen and $5$ bowlers

There are $3$ bags $A, B$ & $C$. Bag $A$ contains $1$ Red & $2$ Green balls, bag $B$ contains $2$ Red & $1$ Green balls and bag $C$ contains only one green ball. One ball is drawn from bag $A$ & put into bag $B$ then one ball is drawn from $B$ & put into bag $C$ & finally one ball is drawn from bag $C$ & put into bag $A$. When this operation is completed, probability that bag $A$ contains $2$ Red & $1$ Green balls, is -

A binary number is made up of $16$ bits. The probability of an incorrect bit appearing is $p$ and the errors in different bits are independent of one another. The probability of forming an incorrect number is