Probability

The probability of forming a 12 persons committee from 4 engineers, 2 doctors and 10 professors containing at least 3 engineers and at least 1 doctor, is

1. 129182
2. 1726
3. 1926
4. 103182

Three distinct numbers are selected randomly from the set \1, 2, 3, , 40\. If the probability, that the selected numbers are in an increasing G.P., is mn, (m, n) = 1, then m + n is equal to .

Two numbers k1 and k2 are randomly chosen from the set of natural numbers. Then, the probability that the value of ik1 + ik2, (i = -1) is non-zero, equals

1. 34
2. 12
3. 14
4. 23

Let S be the set of all the words that can be formed by arranging all the letters of the word GARDEN. From the set S, one word is selected at random. The probability that the selected word will NOT have vowels in alphabetical order is:

1. 14
2. 12
3. 13
4. 23

One die has two faces marked 1 , two faces marked 2 , one face marked 3 and one face marked 4 . Another die has one face marked 1 , two faces marked 2 , two faces marked 3 and one face marked 4. The probability of getting the sum of numbers to be 4 or 5 , when both the dice are thrown together, is

1. 23
2. 35
3. 49
4. 12

A board has 16 squares as shown in the figure : [figure] Out of these 16 squares, two squares are chosen at random. The probability that they have no side in common is :

1. 35
2. 45
3. 2330
4. 710

Let a, b and c denote the outcome of three independent rolls of a fair tetrahedral die, whose four faces are marked 1, 2, 3, 4. If the probability that ax2 + bx + c = 0 has all real roots is mn, (m, n) = 1, then m + n is equal to .

If an unbiased dice is rolled thrice, then the probability of getting a greater number in the ith roll than the number obtained in the (i - 1)th roll, i = 2, 3, is equal to

1. 5/54
2. 2/54
3. 1/54
4. 3/54

Let the sum of two positive integers be 24. If the probability, that their product is not less than 34 times their greatest possible product, is mn, where (m, n) = 1, then n - m equals

1. 10
2. 11
3. 9
4. 8

If three letters can be posted to any one of the 5 different addresses, then the probability that the three letters are posted to exactly two addresses is :

1. 1825
2. 1225
3. 625
4. 425