Random Experiments

If $A$ and $B$ are two mutually exclusive events of a random experiment and $P\left(\text{not}A\right)=0.9,P\left(A\text{or}B\right)=0.65$, find $P\left(B\right)$.

Three six faced fair dice are thrown together. The probability that the sum of the numbers appearing on the dice is $k\left(3\le k\le 8\right)$ , is

Fifteen coupons are numbered $1,2,........15,$ respectively. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on selected coupons is not greater than $9$, is

The probability that a man can hit a target is $\frac{3}{4}.$ He tries$5$ times. The probability that he will hit the target at least three times is

If a person throws 3 dice, the probability of getting sum of digit exactly 15 is-

Two dice are thrown together. The probability of getting the sum of digits as a multiple of 4 is

A bag contains 5 brown and 4 white socks. A man pulls out 2 socks. The probability that they are of the same colour is

A five-digit number is formed by the digits $1, 2, 3, 4, 5, 6$ and $8$. The probability that the number has even digit at both ends when the repetition of digits is not allowed.

A card is drawn from a well - shuffled pack of 52 cards. If the chance that card drawn is either a black card or king of non -black card is P. Then 13P-6 is equal to :

Two dice are rolled simultaneously. Then the probability of obtaining the sum of number occurring on both the dice a prime number greater than 6 is equal to :

If the chance that a leap year will have $53$ Sunday or $53$ Monday is $P$. Then number $14P +1$

Two dice are thrown simultaneously. If the probability of obtaining a number on the first dice less than that of number occuring on second dice is P. Then 24P-10 is equal to :

A card is drawn from a well shuffled pack of $52$ cards. If the chance that card drawn is either a black card or king of non -black card is $P,$ then $13P-6$ is equal to 

Two dice are rolled simultaneously. Then the probability of obtaining the sum of number occurring on both the dice a prime number greater than 6 is equal to :

A bag contains $3$ red balls, $5$ yellow balls and $4$ green balls. $3$ balls are drawn randomly. What is the probability that the balls drawn contain no yellow ball?

A coin is tossed three times. The probability of getting head and tail alternatively, is

In a book of $500$ pages, it is found that there are $250$ typing errors. Assume that poisson law holds for the number of errors per page. Then, the probability that a random sample of $2$ pages will contain no error, is

Four dice are rolled. The number of possible outcomes in which at least one dice shows 2 is

A fair coin is tossed repeatedly. If the tail appears on first four tosses, then the probability of the head appearing on the fifth toss, equals

The probability that the two digit number formed by digit $1,2,3,4,5$, is divisible by $4$ (while repetition of digit is allowed), is