To find the probability of drawing a ticket that is either green or has a number greater than four, let's break down the problem step-by-step:
### Step 1: Determine the Total Number of Tickets
The bag contains:
- Five yellow tickets numbered one to five.
- Five green tickets numbered one to five.
The total number of tickets in the bag is:
[tex]\[ 5 \, \text{(yellow)} + 5 \, \text{(green)} = 10 \, \text{tickets} \][/tex]
### Step 2: Determine the Number of Favorable Outcomes
We need to count the tickets that are either green or have a number greater than four.
1. Green Tickets: There are 5 green tickets.
2. Tickets Numbered Greater Than Four:
- Yellow tickets that are greater than four: There is only one yellow ticket greater than four (number 5).
- Green tickets that are greater than four: There is only one green ticket greater than four (number 5).
Adding these favorable outcomes:
- 5 (green tickets)
- 1 (yellow ticket numbered 5)
Since the green ticket numbered 5 is already counted within the green tickets, we should not count it again. The correct count now is:
[tex]\[ 5 \, \text{(green tickets)} + 1 \, \text{(yellow ticket numbered 5)} = 6 \, \text{favorable outcomes} \][/tex]
### Step 3: Calculate the Probability
The probability [tex]\( P \)[/tex] is given by the ratio of the number of favorable outcomes to the total number of tickets. We calculated the favorable outcomes as 6 and the total number of tickets as 10. Therefore, the probability is:
[tex]\[ P = \frac{\text{number of favorable outcomes}}{\text{total number of tickets}} = \frac{6}{10} = 0.6 \][/tex]
### Step 4: Convert the Probability to a Fraction
The fraction equivalent to 0.6 is:
[tex]\[ 0.6 = \frac{6}{10} = \frac{3}{5} \][/tex]
Thus, the probability that you pick a ticket that is either green or has a number greater than four is:
[tex]\[ \frac{3}{5} \][/tex]
### Final Answer
The correct option is:
C. [tex]\(\frac{3}{5}\)[/tex]
