Probability of an Event的问题。请各位帮个忙。

ting_006

A dice is loaded in such a way that an even number is twice as likely to occur as an odd number. If
E is the event that a number less than 4 occurs on a single toss of the dice, find P(E).



Ans:4/9

leong321

tree diagram
P(<4)=P(odd n 1)+P(even n2)+P(odd n 3)
       =1/3(1/3)+2/3(1/3)+1/3(1/3)
       =4/9  
我是这样做的..

peaceboy

p(odd) = a
p(even) = 2a

a+a+a+2a+2a+2a = 1
9a=1
a=1/9

P(E<4) = P(odd) +P(even) + P(odd)
            =1/9 + 2/9 +1/9
            = 4/9