In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary.

In a musical chair game, the person playing the music has been advised to stop playing the music at any time within 2 minutes after she starts playing. What is the probability that the music will stop within the first half-minute after starting?

Each of the n urns contains 4 white and 6 black balls. The (n + 1)th urn contains 5 white and 5 black balls. One of the n + 1 urns is chosen at random and two balls turn out to be black. If the probability that the (n + 1)th urn was chosen to draw the balls is 1/16, then find the value of n.

Suppose a girl throws a die. If she gets a 5 or 6, she tosses a coin three times and notes the number of heads. If she gets 1, 2, 3 or 4, she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head, what is the probability that she threw 1, 2, 3 or 4 with the die?

A box contains 12 red and 6 white balls. Balls are drawn from the bag one at a time without replacement. If in 6 draws, there are at least 4 white balls, find the probability the exactly one white ball is drawn in the next two draws. (Binomial coefficients can be left as such.)

A bag containsa red ball a blue ball and an yellow ball, all the balls being of the same size. Manasa takes out a ball fromthe bag without looking into it. What is the probability that she takes a (i) yellow ball? (ii) red ball? (iii) blue ball?

A box contains 12 balls out of which x are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball? If 6 more black balls are put in the box, the probability of drawing a black ball is now double of what it was before. Find x.

Two players P_(1)and P_(2) are playing the final of a chess championship, which consists of a series of matches. Probability of P_(1) winning a match is 2/3 and that of P_(2) is 1/3. Thus winner will be the one who is ahead by 2 games as compared to the other player and wins at least 6 games. Now, if the player P_(2) wins the first four matches, find the probability of P_(1) wining the championship.

A batsman scores exactly a century by hitting fours and sixes in 20 consecutive balls. In how many different ways can he do it if some balls may not yield runs and the order of boundaries and over boundaries are taken into account?

A cricket ball of mass 150 g, moving at 12 m cdot s^(-1) , is hit by a cricket bat. The ball recoils with a velocity of 20 m cdot s^(-1) . If the bat was in contact with the ball for 0.01 s, find the average force imparted on the ball by the bat.