Which events are independent? A.) you choose 2 different ice cream flavors B.) you study English 20 minutes nightly then you get an A on the next test C.) you draw card from a deck and replace it and draw second D.) you draw card and don’t replace it then you draw another

An assembly consists of two mechanical components. suppose that the probabilities that the first and second components meet specifications are 0.87 and 0.84. assume that the components are independent. determine the probability mass function of the number of components in the assembly that meet specifications. x

Asmall (but heavy) particle placed in a glass of water will follow a zigzag motion because the particle will bounce off of the water molecules it meets. this is called brownian motion. a physicist simulates this on a computer, by varying the distance a particle can travel (called the mean free length), on average, before it collides with a water molecule and assigning the change in motion to be one of 8 directions, each with a similar probability. by running the simulated particle (with the same mean free length) many times she determines that it should take 15 seconds, on average, for the particle to fall to the bottom, with a standard deviation of 1.5 seconds. next she lets a real particle fall through a glass of water and finds that it took 18 seconds. what does she conclude, and why?

Li buys supplies so he can make and sell key chains. he begins to make a profit only after he sells 4 key chains. what point on the graph makes the most sense in this situation?