UpStudy Free Solution:

To determine the probability that the drawn ping pong ball's number contains two digits, we first need to identify how many of the fifteen numbers (1 through 15) have two digits.

The two-digit numbers within the range 1 to 15 are: 10, 11, 12, 13, 14, and 15. There are 6 such numbers.

The total number of ping pong balls is 15.

The probability of drawing a ping pong ball with a two-digit number is therefore the number of two-digit numbers divided by the total number of ping pong balls:

\[\text { Probability} = \frac { \text { Number of two- digit numbers} } { \text { Total number of ping pong balls} } = \frac { 6} { 15} \]

Simplifying the fraction:

\[\frac { 6} { 15} = \frac { 2} { 5} \]

So, the probability that the drawn ping pong ball's number contains two digits is:

\[\boxed{ \frac { 2} { 5} } \]

Thus, the correct answer is:

B. \(\frac { 2} { 5} \)

Supplemental Knowledge

Probability is a measure of the likelihood that an event will occur. It is quantified as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. The probability \(P\) of an event \(E\) occurring is given by:

\[P( E) = \frac { \text { Number of favorable outcomes} } { \text { Total number of possible outcomes} } \]

In this specific problem, we are dealing with a simple probability scenario where we need to determine the likelihood of drawing a ping pong ball with a two-digit number from a set of numbered balls.

To break it down:

- Favorable outcomes: These are the numbers that meet our criteria (two-digit numbers in this case).

- Total possible outcomes: This is the total number of items in our sample space (all numbered ping pong balls).

For the range from 1 to 15:

- Two-digit numbers: \(10, 11, 12, 13, 14, 15\)

- Total two-digit numbers: \(6\)

- Total numbers: \(15\)

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