propbability

1)a) P(the sum of the faces is 3)
= P(1,2) + P(2,1)
= (1/6)^2 + (1/6)^2
= 1/18
b) P(the sum of the faces is 7)
= P(1,6) + P(6,1) + P(2,5) + P(5,2) + P(3,4) + P(4,3)
= 6 * (1/6)^2
= 1/6
c) P(the sum of the faces is 3 or 7)
= P(the sum of the faces is 3) + P(the sum of the faces is 7)
= 1/18 + 1/6
= 2/9


2)a) P(4 heads will turn up)
= (1/2)^4 = 1/16
b) P(2 heads and 2 tails will turn up)
there are 4 positions , 2 heads have 4C2 = 6 ways.
= (4C2)(1/2)^4 = 6(1/16)
= 3/8
c) P(1head and 3 tails will turn up)
there are 4 positions , 1 head have 4 ways.
= 4(1/2)^4
= 1/4

3a) P(two persons selected at random both own cars)
= 1/4 x 1/4 = 1/16
b) P(of two persons selected at random, only one owns a car)
= (3/4 x 1/4) + (1/4 x 3/4) = 3/8
c) P(three persons selected at random all own cars)
= (1/4)^3 = 1/64
d) P(of three persons selected at random, none owns a car)
= (3/4)^3 = 27/64
e) P(of three persons selected at random, exactlyone owns a car)
= P(The 1st one own a car) + P(The 2nd one own a car) + P(The 3rd one own a car)
= (1/4)(3/4)(3/4) + (3/4)(1/4)(3/4) + (3/4)(3/4)(1/4)
= 3(1/4)(3/4)^2
= 27/64