Sure, let's solve this problem step-by-step:
1. Identify the total number of tickets in the bag:
- There are 20 red tickets.
- There are 12 blue tickets.
- Therefore, the total number of tickets = 20 (red) + 12 (blue) = 32 tickets.
2. Determine the number of blue tickets:
- The number of blue tickets is 12.
3. Calculate the probability of selecting a blue ticket:
- Probability is given by the number of favorable outcomes divided by the total number of possible outcomes.
- The probability P of selecting a blue ticket = Number of blue tickets / Total number of tickets = 12 / 32.
4. Simplify the fraction:
- First, simplify 12 / 32 by finding the greatest common divisor (GCD).
- The GCD of 12 and 32 is 4.
- When you divide both the numerator and the denominator by 4, you get:
- [tex]\( \frac{12}{32} \)[/tex]
- [tex]\( = \frac{12 \div 4}{32 \div 4} \)[/tex]
- [tex]\( = \frac{3}{8} \)[/tex]
So, the probability of randomly selecting a blue ticket from the bag is [tex]\( \frac{3}{8} \)[/tex].
Therefore, the best answer is:
A. [tex]\( \frac{3}{8} \)[/tex]
