Short Answer TypeA and B throw a pair of dice alternately, till one of them gets a total of 10 and wins the game. Find their respective probabilities of winning, if A starts first.
Long Answer TypeThree numbers are selected at random (without replacement) from first six positive integers. Let X denote the largest of the three numbers obtained. Find the probability distribution of X.Also, find the mean and variance of the distribution.
Short Answer TypeIn a set of 10 coins, 2 coins are with heads on both the sides. A coin is selected at random from this set and tossed five times. If all the five times, the result was heads, find the probability that the selected coin had heads on both the sides
How many times must a fair coin be tossed so that the probability of getting at least one head is more than 80%?
Long Answer TypeTwo the numbers are selected at random (without replacement) from first six positive integers. Let X denote the larger of the two numbers obtained. Find the probability distribution of X. Find the mean and variance of this distribution.
Short Answer TypeAn experiment succeeds thrice as often as it fails. Find the probability that in the next five trials, there will be at least 3 successes.
Long Answer TypeThere are three coins. One is a two-headed coin (having head on both faces), another is a biased coin that comes up heads 75% of the times and third is also a biased coin that comes up tails 40% of the times. One of The three coins is chosen at random and tossed, and it shows heads. What is the probability that it was the two-headed coin?
Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find the probability distribution of the random variable X, and hence find the mean of the distribution.
Short Answer TypeA speaks truth in 60% of the cases, while B in 90% of the cases. In what percent of cases are they likely to contradict each other in stating the same fact? In the cases of contradiction do you think, the statement of B will carry more weight as he speaks truth in more number of cases than A?
Let the probability that A and B speak truth be P(A) and P(B) respectively.
Therefore, 
A and B can contradict in stating a fact when one is speaking the truth and other is not speaking the truth.
Case 1: A is speaking the truth and B is not speaking the truth.
Case 2: A is not speaking the truth and B is speaking the truth.
Required Probability = 
Percentage of cases in which they are likely to contradict in stating the same fact =
From case 1, it is clear that is not necessary that the statement of B will carry more weight as he speaks truth in more number of cases than A.
Long Answer TypeAssume that the chances of a patient having a heart attack is 40%. Assuming that a meditation and yoga course reduces the risk of heart attack by 30% and prescription of certain drug reduces its chance by 25%. At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options, the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation
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