Probability · Question 1

A coin is tossed 8 times. If the probability that exactly 4 heads appear in the first six tosses and exactly 3 heads appear in the last five tosses is p, then 96p is equal to .

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