For a six sides dice: Possible numbers are: 1, 2, 3, 4, 5, and 6 Total of 6 possible numbers Possible even number outcomes are: 2, 4, and 6 Total of 3 outcomes out of 6 possibilities Probability that the roll is a even number, p(A) = 3/6 p(A) = 3/6 = 1/2
<span>Possible outcomes greater than 4 are: 5 and 6 Total of 2 outcomes out of 6 possibilities </span>Probability that the roll is a number greater than 4, p(B) = 2/6 p(B) = 2/6 = 1/3
The probability that the first roll is a even number and the second roll is a number greater than 4 = p(A and B) p(A and B) = p(A) x p(B)
p(A) = 1/2 p(B) = 1/3 p(A and B) = p(A) x p(B) = 1/2 * 1/3 = 1/6
![\frac{1}{ \frac{343}{3} } \int\limits^7_0 \int\limits^{x^2}_0 {4x\sin(y)} \, dydx = -\frac{3}{343} \int\limits^7_0 {4x\cos(x^2)} \, dx \\ \\ =-\frac{3}{343} \int\limits^{49}_0 {2\cos(t)} \, dt=-\frac{6}{343} \left[\sin(t)\right]_0^{49} \, dt=-\frac{6}{343}\sin49](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B%20%5Cfrac%7B343%7D%7B3%7D%20%7D%20%20%5Cint%5Climits%5E7_0%20%20%5Cint%5Climits%5E%7Bx%5E2%7D_0%20%7B4x%5Csin%28y%29%7D%20%5C%2C%20dydx%20%20%3D%20-%5Cfrac%7B3%7D%7B343%7D%20%20%5Cint%5Climits%5E7_0%20%7B4x%5Ccos%28x%5E2%29%7D%20%5C%2C%20dx%20%20%5C%5C%20%20%5C%5C%20%3D-%5Cfrac%7B3%7D%7B343%7D%20%5Cint%5Climits%5E%7B49%7D_0%20%7B2%5Ccos%28t%29%7D%20%5C%2C%20dt%3D-%5Cfrac%7B6%7D%7B343%7D%20%5Cleft%5B%5Csin%28t%29%5Cright%5D_0%5E%7B49%7D%20%5C%2C%20dt%3D-%5Cfrac%7B6%7D%7B343%7D%5Csin49)