概率...快快"

1) Let the center of the coin be C, player will win if C is at least 2cm away from all 4 sides of the square it lies

Within a 8cm x 8cm square, C is 2cm away from each side when it lies within the 4cm x 4cm zone in the centre of the 8cm x 8cm square (try to draw out the graph and you'll see!)

Since the coin have equal chance to land on anywhere within any square, probability players will win
= area of the 4cm x 4cm square (win zone) / area of the 8cm x 8cm square (possible zone)
= 16 / 64
= 1 / 4



2)

(a) since p + q = 1 and p:q = 2:3

on solving, p=0.4 and q=0.6

(b)

Since two throw of dices are independent of each other,

Prob(both dice shows odd outcome)
= Prob(a dice shows odd outcome)^2
= p^2
= 0.16

Similarly, Prob(both dices shows even outcome)
=q^2
= 0.36

Prob(one show odd and one show even)
= 1 - 0.16 - 0.36
= 0.48



3)

(a) Let number of boys be x, so number of girls is 1.2x

since 30< total number of boy and girl < 40

30 < x + 1.2x < 40
30 < 2.2x < 40
13.6 < x < 18.2

Since x must be an integer

x = 14 or 15 or 16 or 17 or 18

And since number of girls is 1.2x, 1.2x must be an integer as well

Therefore, x can only be 15

i.e. 15 boys, 18 girls

(b)

Prob (one boy and one girl)
= prob (1st is a boy and 2nd is a girl) + prob(1st is a girl and 2nd is a boy)
= 15/33 x 18/32 + 18/33 x 15/32
= 45 / 88



4)

(a) Prob (get 3 marks) = Prob(3 correct out of 3 questions) = 0.6^3 = 0.216

(b) Prob (get 0 marks) = Prob(0 correct out of 3 questions) = (1-0.6)^3 = 0.4^3 = 0.064

(c) Prob (get 1 mark) = Prob(1st question correct but 2nd and 3rd are wrong) + Prob(2nd question correct but 1st and 3rd are wrong) + Prob(3rd question correct but 1st and 2nd are wrong) = 3 x (0.6 x 0.4 x 0.4) = 0.288

(d) Prob (get 2 marks) = 3 x (0.6 x 0.6 x 0.4) = 0.432

Note that 4 answers add up to 1 (0.216 + 0.064 + 0.288 + 0.432 = 1)

1) (2 X 2 X 3.14) /8 X 8 ~19.6
2) P=2/2+3
=0.4
Q=3/2+3
=0.6