To find the probability that a randomly chosen ticket will award a larger prize, we can proceed as follows:
1. Determine the probability of drawing a winning ticket:
- There are 10 tickets in total, and 6 out of the 10 tickets are winning tickets.
- The probability of drawing a winning ticket is:
[tex]\[
\frac{6}{10} = 0.6
\][/tex]
2. Determine the probability that a winning ticket will award a larger prize:
- Of the winning tickets, 1 out of every 3 tickets is a larger prize ticket.
- The probability that a winning ticket is a larger prize ticket is:
[tex]\[
\frac{1}{3}
\][/tex]
3. Calculate the overall probability of drawing a larger prize ticket:
- To find the overall probability, multiply the probability of drawing a winning ticket by the probability of that winning ticket being a larger prize ticket:
[tex]\[
0.6 \times \frac{1}{3} = 0.2
\][/tex]
Expressing 0.2 as a fraction, we get:
[tex]\[
0.2 = \frac{2}{10} = \frac{1}{5}
\][/tex]
Thus, the probability that a randomly chosen ticket will award a larger prize is:
[tex]\[
\boxed{\frac{1}{5}}
\][/tex]
