Probability

From a month of 31 days, 3 different dates are selected at random. If the probability that these dates are in an increasing A.P. is equal to ab, where a, b N and (a, b)=1, then a+b is equal to .

Let a, b, c \1, 2, 3, 4\. If the probability, that ax2+2 2 bx+c>0 for all x R, is mn, (m, n)=1, then m+n is equal to .

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

Let S be a set of 5 elements and P(S) denote the power set of S. Let E be an event of choosing an ordered pair (A, B) from the set P(S) P(S) such that A B = . If the probability of the event E is 3p2q, where p, q N, then p + q is equal to .

From the first 100 natural numbers, two numbers first a and then b are selected randomly without replacement. If the probability that a - b 10 is mn, (m, n) = 1, then m + n is equal to .

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

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