Statistics Practice

Question

You pick any number in the interval (0,3). What is the probability that the number you chose has 3 has the first digit after the decimal point? This is not a homework problem. It is a practice problem in a study guide that I cannot solve.

Answer 1

You may understand this problem as blocks of $3$ (rows) by $10$ (columns). $3$ rows means the ones digit is $0, 1,$ or $2$. 10 columns means the decimal part starts with $.0, .1, .2, .3, .4, .5, .6, .7, .8$, and $.9$. Therefore, you have thirty blocks.

$0.0, 0.1, 0.2, 0.3, ...0.9$

$1.0, 1.1, 1.2, 1.3, ...1.9$

$2.0, 2.1, 2.2, 2.3, ...2.9$

Therefore, the probability for the numbers where the decimal part starts with 3 (e.g., $0.3, 1.3, 2.3$) are three blocks out of 30 blocks.

$\frac{3}{30}=\frac{1}{10}$