Mama Temte bakes six pies a day that cost​ $2 each to produce. On 37​% of the days she sells only two pies. On 33​% of the​ days, she sells 4​ pies, and on the remaining 30​% of the​ days, she sells all six pies. If Mama Temte sells her pies for $6 ​each, what is her expected profit for a​ day's worth of​ pies? [Assume that any leftover pies are given​ away.]