Có hai hộp bút màu. Hộp thứ nhất có 6 bút đỏ và 4 bút xanh, hộp thứ hai có 7 bút đỏ và 3 bút xanh. Chọn ngẫu nhiên 1 hộp và từ đó lấy ngẫu nhiên ra 2 cái bút.
a) Tìm xác suất để lấy được 3 bút màu đỏ;
b) Giả sử đã lấy được 3 bút màu đỏ. Tìm xác suất để đó là 3 bút màu đỏ đó là của hộp thứ hai.

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?

What is the missing step in this proof ?

Zoey made 5 1/2 cups of trail mix for a camping trip. she wants to divide the trail mix into 3/4 cup servings. a. ten people are going on the trip. can zoey make enough 3/4 cup servings so that each person gets one serving? b. what size would the servings need to be for everyone to have a serving?