Probability

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 .

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 .

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 .

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 .