class 12

Math

Algebra

Probability I

One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is

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A cube having all of its sides painted is cut by two horizontal, two vertical, and other two planes so as to form 27 cubes all having the same dimensions. Of these cubes, a cube is selected at random. The probability that the cube selected has none of its sides painted is

There are eight girls among whom two are sisters, all of them are so to sit on a round table. Find the probability that the two sisters do not sit together.

A shoping mall is running a scheme: Each packet of detergent SURF contains a coupon which bears letter of the word SURF, if a person buys at least four packets of detergent SURF, and produce all the letters of the word SURF, then he gets one free packet of detergent. If a person buys 8 such packets at a time, then the number of different combinations of coupon he has is

Out of 3n consecutive integers, three are selected at random. Find the probability that their sum is divisible by 3.

Find the probability that a leap year will have 53 Fridays or 53 Saturdays.

In how many ways three girls and nine boys can be seated in two vans, each having numbered seats, 3 in the front and 4 at the back ? How many seating arrangements are possible if 3 girls should sit together in a back row on adjacent seats? Now, if all the seating arrangements are equally likely, what is the probability of 3 girls sitting together in a back row on adjacent seats ?

A dice is loaded so that the probability of a face I is proportional to $i_{2}$ , I = 1, 2, …, 6. Then find the probability of occurring a prime number when the dice is rolled.

Dialing a telephone number an old man forgets the last two digits remembering only that these are different dialed at random. The probability that the number is dialed correctly is