A group of women and men line up for a photograph. Find the probability that at least two people of the same gender are adjacent if there are (a) 5 men and 4 women; (b) 4 men and 4 women. A “loaded”...

A group of women and men line up for a photograph. Find the probability that at least two people of the same gender are adjacent if there are (a) 5 men and 4 women; (b) 4 men and 4 women.

A “loaded” die has the property that the numbers 1 to 5 are equally likely but the number 6 is three times as likely to occur as any of the others. What is the probability that the die comes up even?