Probability test 1

A hat contains 20 tickets, each with a different number from 1 to 20. If 4 tickets are drawn at
random, what is the probability that the largest number is 15 and the smallest number is 9?

A number X is chosen at random from the series
2, 5, 8, 11 . . ., 299
and another number Y is chosen from the series
3, 7, 11, . . ., 399.
What is the probability P(X = Y)?

A certain type of missile hits its target 30% of the time. Determine the minimum number of
missiles that must be shot at a certain target in order to obtain a change higher than 80% of hitting the target.

Three people, X, Y, Z, in order, roll a fair die. The first one to roll an even number wins and the game is ended. What is the probability that X will win?

A sequence of independent trials is performed by rolling a pair of fair dice. What is the probability that an 8 will be rolled before rolling a 7?

A simple board game has four fields A, B, C, and D. Once you end up on field A you have won and once you end up on field B you have lost. From fields C and D you move to other fields by flipping a coin. If you are on field C and you throw a head, then you move to field A, otherwise to field D. From field D, you move to field C if you throw a head, and otherwise you mover to field B. Suppose that you start in field D. What is the probability that you will win (i.e., what is the probability that you will end up on field A)?

1. There are 3 ants at 3 corners of a triangle, they randomly start moving towards another corner.

What is the probability that they don't collide?

Two identical pack of cards A and B are shuffled thoroughly. One card is picked from A and shuffled with B. The top card from pack A is turned up. If this is the Queen of Hearts, what are the chances that the top card in B will be the King of Hearts?

A box contains three coins, two of them fair and one two-headed. A coin is selected at random and tossed twice. If heads appears both times, what is the probability that the coin is two-headed?

In the library there are 8 books by Stephen Covey and 1 book by Vinay Singh in shelf A. At the same time, there are 5 books by Stephen Covey in shelf B. One book is moved from shelf A to B. A student picks up a book from shelf B. Find the probability that the book by Vinay Singh is taken by the student.

A fair die is tossed six times. Find the probability of getting a third six on the sixth throw.

A and B are two candidates seeking admission to the IIMs. The probability that A is selected is 0.5 and the probability that both A and B are selected is at most 0.3. Is it possible that the probability of B getting selected is 0.9?

Two small squares on a chess board are chosen at random. Find the probability that they have a common side.

One hundred identical coins each with probability P of showing up heads are tossed once. If 0<p<1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then value of P is?

A hat contains three tickets, numbered 1, 2 and 3. The tickets are drawn from the box one at a time. Find the probability that the ordinal number of at least one ticket coincides with its own number.

Seven white balls and three black balls are randomly placed in a row. Find the probability that no two black balls are placed adjacent to each other.

12 persons are seated around a round table. What is the probability that two particular persons sit together?

Ten tickets are numbered 1, 2, 3 ..., 10. Six tickets are selected at random one at a time with replacement. The probability that the largest number appearing on the selected ticket is 7 is?

If the integers m and n are chosen at random from 1 to 100, then the probability that a number of the form 7^m + 7^n is divisible by 5 is?

A problem on mathematics is given to three students whose chances of solving it are 1/2, 1/3 and Πrespectively. What is the chance that the problem will be solved?