Probability

A six faced die is so biased that it is twice as likely to show an odd number as an even number when rolled. The probability that the sum of the numbers on the upturned faces is even when the die is thrown twice is

A normal coin tossed repeatedly until two consecutive heads is obtained. the probability two consecutive heads occurs on the seventh and eight flips is equal to

There are three bags, $B_{1}, B_{2}$ and $B_{3}$ containing $2$ Red and $3$ White, $5$ Red and $5$ White, $3$ Red and $2$ White balls respectively. A ball is drawn from the bag $B_{1}$ and placed in bag $B_{2}$ then a ball is drawn from bag $B_{3}$. Find the probability that both the drawn ball is white

From a pack of $52\ cards$, face cards and tens are removed and kept aside, then a card is drawn at random from the remaining cards. If A: The events that the card is drawn is an ace. H: The events that the card is drawn is a heart.S: the events that the card is drawn is a spade. Then, which of the following holds?

Three balls are drawn at random from a collection of $7$ white, $12$ green and $4$ red balls. The probability that each is different colour is

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

A dice is rolled 4 times,the numbers appearing are listed. The number of different throws, such that the largest number appearing in the list is not 4, is:

A bag contains $20$ cards $10$ of these cards have letter $'E'$ $5$ have letter $'I'$ and other $5$ have letter $'A'$ printed on them, if five cards are drawn one by one and are kept in same order aside then probability of making the words $AIEEE$ is

Two cards are drawn successively with replacement from a well-shuffled deck of $52$ cards. Let $X$ denote the random variable of number of aces obtained in the two drawn cards. Then $P(X = 1) + P(X = 2)$ equals