A bag contains five yellow tickets numbered one to five. The bag also contains five green tickets numbered one to five. You randomly pick a ticket. It is green or has a number greater than four. Find the probability of this occurring.

A. [tex]\frac{9}{10}[/tex]
B. [tex]\frac{3}{4}[/tex]
C. [tex]\frac{3}{5}[/tex]
D. [tex]\frac{1}{3}[/tex]



Answer :

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]