India and Australia play a series of 7 one-day matches. Each team has equal probability of winning a match. No match ends in a draw. If the probability that India wins atleast three consecutive matches can be expressed as `(p)/(q)` where p and q are relatively prime positive integers. Find the unit digit of p.

India and Pakistan play a 5 match test series of hockey, the probability that India wins at least three matches is

Mr. A writes an article. The article originally is error free. Each day Mr. B introduces one new error into the article. At the end of the day, Mr. A checks the article and has (2)/(3) chance of catching each individual error still in the article. After 3 days, the probability that the article is error free can be expressed as (p)/(q) where p and q are relatively prime positive integers. Let lambda=q-p , then find the sum of the digits of lambda .

Assume that for every person the probability that he has exactly one child, exactly 2 children and exactly 3 children are (1)/(4), (1)/(2) and (1)/(4) respectively . The probability that a person will have 4 grand children can be expressed as (p)/(q) where p and q are relatively prime positive integers. Find the value of 5p-q .

India plays 4 matches with Australia. The probability of india winning a match is 3/4 and loosing match is 1/4 . Find the probability of india winning 3^(rd) " time in " 4^(th) match.

Three different numbers are selected at random from the set A={1,2,3,……..,10} . Then the probability that the product of two numbers equal to the third number is (p)/(q) , where p and q are relatively prime positive integers then the value of (p+q) is :