Question 1011646:
a)An integer is choosen at random from the first 200 positive integer. what is the probabililty that the integer chosen is divisible by 6 or by 8??
b)Three horses A,B,C are in a race; A is twice likely to win as B and B is twice as likely to win as C,what is probability that A or B wins??
Answer by mathmate(429)   (Show Source):
You can put this solution on YOUR website!
Question:
a)An integer is choosen at random from the first 200 positive integer. what is the probabililty that the integer chosen is divisible by 6 or by 8??
b)Three horses A,B,C are in a race; A is twice likely to win as B and B is twice as likely to win as C,what is probability that A or B wins??
Solutions:
note: floor(x)=[x]=largest integer that does not exceed x.
a)
between 1 and 200,
floor(200/6)=33 are divisible by 6
floor(200/8)=25 are divisible by 8
floor(200/24)=8 are divisible by 24 (LCM of 6 and 8)
So by the inclusion/exclusion principle, (33+25-8)=50 are divisible by 6 or 8.
b)
P(A)=2P(B)
P(B)=2P(C)
=>
P(A)=4P(C)
or
P(A)+P(B)+P(C)=(4+2+1)P(C)=7P(C)=1
P(C)=1/7
Therefore probability that A or B wins = 1-1/7=6/7
|
|
|
