Consider the data on wafers classified by contamination and…

Consider the data on wafers classified by contamination and location in the table below.   Number of Contamination Particles Center Edge Totals 0 0.28 0.12 0.40 1 0.17 0.03 0.20 2 0.1 0.05 0.15 3 0.06 0.04 0.10 4 0.04 0.01 0.05 5 or more 0.07 0.03 0.10 Totals 0.72 0.28 1   Assume that one wafer is selected at random from this set. Let A denote the event that a wafer contains four or more particles, and let B denote the event that a wafer is from the center of the sputtering tool. Determine P(B|A) 

A game at a carnival involves rolling a fair six-sided die….

A game at a carnival involves rolling a fair six-sided die. The payouts are as follows: If you roll a 6, you win $10. If you roll a 4 or 5, you win $5. If you roll a 1, 2, or 3, you win nothing ($0$). What is the expected payout per roll (i.e. Find the expected value) ?