The minimum number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.8 is


Correct option is


Suppose the coin is tossed n times. Let X be the number of heads obtained. Then X follows a binomial distribution with parameters n and = 1/2. We have P(X ≥ 1) ≥ 0.8       

         ⇒ 1 – P(X = 0) ≥ 0.8


This show that the least value of n is 3.



Two squats are chosen at random on a chessboard. The probability that they have a side in common is


A man is known to speak the truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six is 


A bag contains a white and b black balls. Two players, A and B alternate ydraw a ball from the bag, replacing the ball each time after the draw till one of them draws a white ball and wins the game. A begins the game. If the probability of A winning the game is three times that of B, the ratio ab is


A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the determinant chosen is non – zero is


A fair coin is tossed 100 times. The probability of getting tails an odd number of times is


One hundred identical coins, each with probability of head are tossed once. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, the value of p is


Suppose X follows a binomial distribution with parameters n and p, where 0 < p < 1. If P (X = r)/P(X = n – r) is independent of n for every value ofr, then 


For the three events AB and CP(exactly one of the events A or Boccurs) = P(exactly one of the events B or C occurs) = P(exactly one of the events C or A occurs) = p and P (all the three events occur simultaneously) = p2, where 0 < p < 1/2. Then the probability of at least one of the three events AB and C occurring is


Nine identical balls are numbers 1, 2,…9. Are put in a bag. A draws a ball and gets the number a. the ball is put back the beg. Next B draws a ball gets the number b. The probability that a and b satisfies the inequality a – 2b + 10 > 0 is


An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times. Out of four face times. Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5 is then,