F.5 probablilty

If the three organizations all select a different month,

the 1st organization may choose any month in the year,

the 2nd one must choose a month from the rest 11 months,

and the 3rd one must choose a month from the rest 10 months.


P(1st organization chooses any month in the year) = 12/12 = 1

P(2nd organization chooses a month from the rest 11 months) = 11/12

P(3rd organization chooses a month from the rest 10 months) = 10/12


P(The three organizations all select a different month)

= 1 x (11/12) x (10/12)

= 55/72
=

P = {4[1- (1/30)^3 - 3(1/30)^2]+ 7[1- (1/31)^3 - 3(1/31)^2] + 1[1- (1/28)^3 - 3(1/28)^2] }/12
= (3.986518519 + 6.977912792 + 0.996127915) /12
=0.996713268
=0.997 (3 s.f)

有4個月係30日 7個月係31日 同埋 1個月係28日