$A$ letter is chosen at random from the word $ASSASSINATION$. Find the probability that the letter is a vowel. (in $/13$)

$A$ die is formed so that the probability of getting a number $i$ when it is rolled is proportional to $i$ $(i=1, 2, 3, 4, 5, 6)$. The probability of getting an odd number on the die when it is rolled is

$A$ man alternately tosses a coin and throws a dice,beginning with the coin. The probability that he gets a head in the coin before he gets a $5$ or $6$ in the dice is

An experiment consists of tossing a coin and then throwing it a second time if a head occurs. If a tail occurs on the first toss,then a die is rolled once. Find the sample space.

$A$ die is rolled. Let $E$ be the event "die shows $4$" and $F$ be the event "die shows an even number". Are $E$ and $F$ mutually exclusive?

Person $A$ can solve $90 \%$ of the problems given in the book and Person $B$ can solve $70 \%$. Then,the probability that at least one of them will solve the problem selected at random from the book is