Expected_Sum := 250*0.15; SE_Sum := sqrt(250.)*sqrt(0.15*0.85); Expected_percent := Expected_Sum/250*100; SE_percent := 100*SE_Sum/250; su_14 := (14-15)/SE_percent; p := 3/123; chance_of_0_reds := (1-p)^100.; chance_of_1_red := 100*p*(1-p)^99.; chance_of_2_reds := binomial(100,2)*p^2.*(1-p)^98.; chance_at_least_3 := 1 - (.085 + .212 + .262); Expected_SUM := 100.*p; SE_SUM := evalf( sqrt(100.)*sqrt(p*(1-p)) ); z := (2.5 - Expected_SUM)/SE_SUM; area := (100 - 3.99)/2.; ave := (2+2+5+5+6+7+7+7)/8.; sd := sqrt( (2*(2-ave)^2+2*(5-ave)^2+(6-ave)^2+3*(7-ave)^2)/8. ); expected_sum := 400*ave; se_sum := sqrt(400)*sd; su_2000 := (2000 - expected_sum)/se_sum; su_2080 := (2080 - expected_sum)/se_sum; Area_076 := 54.67: Area_127 := 80.64: chance := Area_076 + (Area_127 - Area_076)/2; ave_box := (1+2+3+4+5+6)/6.; sd_box := sqrt(((1-3.5)^2+(2-3.5)^2+(3-3.5)^2+(4-3.5)^2+(5-3.5)^2+(6-3.5)^2)/6); es := 3*ave_box; se := sqrt(3.)*sd_box; ninefive_in_su := (9.5-es)/se; tenfive_in_su := (10.5 - es)/se; area_0 := 50: area_34 := 27: answer := area_34/2.; exact_chance := 100*27/(6*6*6.); Number_of_ways := binomial(127,56);