1) Given a cube, an ant is placed in a corner and cant move. A spider starts from opposite corner and can move along cube edges in any direction (x,y,z) with probability 1/3. What is the expected number of steps for this spider to get to the ant?

I am getting (8/3)a where a is the length of the side of cube.

Can someone please solve this and confirm?

2) An investment, 16% chance to lose money on a quarter, and each quarter follows i.i.d. normal distribution. Q: what is the probability of losing money by the end of the year?

3) 2, 3, 5, 16, 231...?

4) There are sticks of length 1,2,3...10.we need to join them.Cost for joining x length stick with y length=(x+y).Find the total cost of joining these sticks.

5) A and B run around a circle of 0.5 km.The ratio of A:B is 5:3 in terms of distance covered.Then find the distance of A when it overtakes the 5th round of B?

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