Suppose that 40% of fruit flies possess a certain gene.  We will randomly select fruit flies until we have found 3 flies with the gene.  Let Y = 0, 1, 2, 3, 4, 5,  be the random variable defined as the number of flies we must be select so that we obtain three flies with the gene.  If f(y) denotes the probability function for Y, find f(7).

The circuit shown below operates if and only if there is some path of functional devices from left to right. The probability that each device functions is shown for each device and the devices operate independently of each other. What is the probability that the circuit operates? 0.9 0.9 0.8 0.95 0.95 0.9 (A) None of these (B) 0.5263 (C) 0.1642 (D) 0.9850 (E) 0.9702