Probability

A bag contains 6 blue and 6 green balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each drawn pair consists of one blue and one green ball is :

1. 63925
2. 17231
3. 16231
4. 64925

A man throws a fair coin repeatedly. He gets 10 points for each head he throws and 5 points for each tail he throws. If the probability that he gets exactly 30 points is mn, (m, n)=1, then m+n is equal to :

1. 53
2. 55
3. 107
4. 105

Two distinct numbers a and b are selected at random from 1, 2, 3, , 50. The probability, that their product ab is divisible by 3, is

1. 2721225
2. 5611225
3. 6641225
4. 825

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

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

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

The coefficients a, b, c in the quadratic equation ax2 + bx + c = 0 are chosen from the set \1, 2, 3, 4, 5, 6, 7, 8\. The probability of this equation having repeated roots is :

1. 1128
2. 164
3. 3256
4. 3128

The coefficients a, b, c in the quadratic equation ax2 + bx + c = 0 are from the set \1, 2, 3, 4, 5, 6\. If the probability of this equation having one real root bigger than the other is p, then 216p equals :

1. 38
2. 76
3. 57
4. 19

Two integers x and y are chosen with replacement from the set \0,1,2,3, ,10\. Then the probability that |x-y|>5, is :

1. 31121
2. 60121
3. 62121
4. 30121