College

A fundraiser lottery draws two winners each month from 50 tickets numbered 1 through 50. Margery always puts her age, 34, on her lottery ticket and enters it into the lottery. This month, the number 5 is drawn first and removed from the lottery. What is the probability of drawing the number 34 on the second draw?

A. [tex]\frac{1}{50}[/tex]
B. [tex]\frac{34}{49}[/tex]
C. [tex]\frac{34}{50}[/tex]
D. [tex]\frac{1}{49}[/tex]

Answer :

To find the probability of drawing the number 34 on the second draw, we can follow these steps:

1. Initial Number of Tickets: The lottery begins with 50 tickets, each numbered from 1 to 50.

2. First Draw: The number 5 is drawn initially and removed from the pool. This leaves us with 49 tickets in the lottery.

3. Second Draw: Margery's ticket number, 34, is still in this remaining group of 49 tickets.

4. Probability Calculation: The probability of drawing Margery's ticket number 34 on this second draw is determined by the ratio of the number of favorable outcomes to the total possible outcomes. Since there is only one ticket with the number 34, the number of favorable outcomes is 1. The total number of tickets left is 49.

Therefore, the probability of drawing the number 34 on the second draw is:
[tex]\[ \frac{1}{49} \][/tex]

This matches the numerical result given.