When coin is tossed it comes up heads with probability , whereas coin comes up heads with probability . Suppose one of these coins is randomly chosen and is tossed twice. If both tosses come up heads, what is the probability that coin was tossed? Justify your answer.
In each draw of a lottery, an integer is picked independently at random from the first integers , with replacement. What is the probability that in a sample of successive draws the numbers are drawn in a non-decreasing sequence? Justify your answer.