Justin’s teacher places a ticket with a student’s name in a jar each time they perform an act of kindness. At the end of the week the teacher will draw a ticket from the jar and award a prize. Justin has 13 tickets so far, with a total of 100 in the whole jar. His goal is to have 20 tickets, and he’s estimating the total number of tickets at that point would be about 200. What is the probability of him winning the drawing if he meets his goal?(1 point)

Question

Justin’s teacher places a ticket with a student’s name in a jar each time they perform an act of kindness. At the end of the week the teacher will draw a ticket from the jar and award a prize. Justin has 13 tickets so far, with a total of 100 in the whole jar. His goal is to have 20 tickets, and he’s estimating the total number of tickets at that point would be about 200. What is the probability of him winning the drawing if he meets his goal?(1 point)
Responses

13200
Start Fraction 13 over 200 End Fraction

15
Start Fraction 1 over 5 End Fraction

110
Start Fraction 1 over 10 End Fraction

13100

GPT 3.5 · Answer

The probability of Justin winning the drawing if he meets his goal is 15 (1/5).

Justin currently has 13 tickets out of 100, so the probability of drawing his ticket is 13/100. If he reaches his goal of 20 tickets out of 200, the probability of drawing his ticket will be 20/200 = 1/10.

Therefore, the change in probability is 1/10 - 13/100 = 1/10 - 1/13 = 3/30 - 2.3/30 = 1/30 = 1/5.

So, the probability of Justin winning the drawing if he meets his goal is 1/5.