Ross and Rachel have just tied the knot. The probability that they are happy each day depends on whether they were happy or sad during the last two days, in the following fashion: Last two days Happy Sad HH [ .8 .2 ] HS | .5 .5 | SH | .7 .3 | SS [ .4 .6 ] For example, if the newlyweds were sad two days ago and yesterday they were happy, then there is a 70% chance they will be happy tomorrow and a 30% chance they will be sad tomorrow. On what fraction of days will Ross and Rachel be happy? Solution The probability of Ross and Rachel to be happy during a day is 7/10.