MATHS

27
(a)
P=1-1/4=3/4
(b)
He success in the last shot
The probability that he succeed in the next three shot
=(3/5)(3/5)(3/5)
=27/125
(c)
The probability that he succeed in the first three shot
=1/2*3/5*3/5
=9/50
(ii)
The probability that he missed one in the first three shot
=P(SSF)+P(FSS)+P(SFS) [S:success F:fail]
=1/2*3/5*2/5+1/2*1/4*3/5+1/2*2/5*1/4
=6/50+3/40+2/40
=0.245
(iii)
The probability that he missed one in the first three shot
=P(FFF)
=1/2*3/4*3/4
=9/32
28
(a)
The probability that the patient is still in room A
=3/4
(d)
The probability that all people in room C are nurse
=P(choose nurse in room A)P(choose nurse in room B)
=2/4*3/5
=6/20
=3/10
30
(a)
p:q=2:3
let p=2k,q=3k
p+q=1
so p=0.4,q=0.6
(b)
(i)
P
=(0.4)(0.4)
=0.16
(ii)
P
=P(odd,even)+P(even,odd)
=2(0.4)(0.6)
=0.48
(iii)
P
=(0.6)(0.6)
=0.36
(c)
Let
outcome 1:two odd
outcome 2:one odd one even
outcome 3:two even
The choice to get points greater 20 are
outcome 1,outcome 1,outcome 1
outcome 1,outcome 1,outcome 2
outcome 1,outcome 2,outcome 1
outcome 2,outcome 1,outcome 1
outcome 1,outcome 1,outcome 3
outcome 1,outcome 3,outcome 1
outcome 3,outcome 1,outcome 1
So the probability that the points larger than 20
=(0.16)^3+3*(0.16)^2(0.48)+3*(0.16)^2(0.36)
=0.068608
The choice to get points greater 10 are
outcome 3,outcome 3,outcome 3
outcome 3,outcome 3,outcome 2
outcome 3,outcome 2,outcome 3
outcome 2,outcome 3,outcome 3
So the probability that the points larger than 20
=(0.36)^3+3*(0.36)^2(0.48)
=0.23328