Sally has two coins. The first coin is a fair coin and the second coin is biased. The biased coin comes up heads with probabilit
y .75 and tails with probability .25. She selects a coin at random and flips the coin ten times. The results of the coin flips are mutually independent. The result of the 10 flips is: T,T,H,T,H,T,T,T,H,T. What is the probability that she selected the biased coin?
''What is the probability that she selected the biased coin?”
When we have n possible outcomes of an event and all of them have the same probability of appearance, then in theory each possibility has a probability 1/n of being the result of the event.
In this case the event is choosing randomly a coin out of 2, so no matter what the biased coin is or the results we get when we toss it, the probability of choosing the biased coin is ½ = 0.5 or 50%.
Consider c as the cost of the widget so that our given equation is c = 0.1w^2 + 20w Take the derivate of the equation. d/dt (c = 0.1w^2 + 20w) dc/dt = 0.2w + 20 Given dc/dt = $16000 per month, the number of widgets would contain: 16000 = 0.2w + 20 -0.2w = 20 - 16000 -0.2w = -15980 w = 79900 widgets
