Probability Question 275
Question: One ticket is selected at random from 100 tickets numbered 00, 01, 02,?.98, 99, if, $ x_1 $ and $ x_2 $ denotes the sum and product of the digits on the tickets, then $ P(x_1=9/x_2=0) $ is equal to
Options:
A) 2/19
B) 19/100
C) 1/50
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Let the number selected by xy.
Then $ x+y=9,0\le x,y\le 9 $ and $ xy=0\Rightarrow x=0,y=9 $ or $ y=0,x=9 $
$ P(x_1=9/x_2=0)=\frac{P(x_1=9\cap x_2=0)}{P(x_2=0)} $
Now, $ P(x_2=0)=\frac{19}{100} $ and $ P(x_1=9\cap x_2=0)=\frac{2}{100} $
$ \Rightarrow P(x_1=9/x_2=0)=\frac{2/100}{19/100}=\frac{2}{19}. $
BETA
