Let A and B be two tests performed by a randomized algorithm, each of which eith

Question

Let A and B be two tests performed by a randomized algorithm, each of which either succeeds or fails. The two tests need not be independent. Let the probability of failure for A be 1/2, and for B be 1/4, Which of the following values could possibly be the probability that both tests fail? Select all that apply. 81/100 21/100 61/100 1/100 41/100 Not all dice have six sides. In fact, 4-, 6-, 8-, 10-, 12- and 20-sided are all fairly easy to design. Suppose that I have one of each of these kinds of dice, and each one has sides numbered from 1 to k, where k is the number of sides on the die. If I roll all of the dice together once, what is the expectation of the sum of the numbers I will get?

Explanation / Answer

a)P(A) = 1/2

P(B) = 1/4

Max value of P(A n B) = min(P(A),P(B)) = 1/4 =25/100

so only possible value of both fails = 21/100

b)Expected value of k sided dice = (1/k)(k(k+1)/2) =(k+1)/2

Expected value of sum of dice = 5/2+7/2+9/2+11/2+13/2+21/2 = 66/2=33

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