To determine the probability that a randomly chosen ticket will award a larger prize, we need to perform the following steps:
1. Calculate the probability of getting a winning ticket.
Given that 6 out of every 10 tickets are winning tickets, the probability of selecting a winning ticket is:
[tex]\[
\text{Probability of winning ticket} = \frac{6}{10} = \frac{3}{5}
\][/tex]
2. Calculate the probability that a winning ticket awards a larger prize.
Given that 1 out of every 3 winning tickets awards a larger prize, the probability of a winning ticket awarding a larger prize is:
[tex]\[
\text{Probability of a larger prize from winning ticket} = \frac{1}{3}
\][/tex]
3. Calculate the combined probability that a randomly chosen ticket will award a larger prize.
We need to find the probability of both events happening together:
- drawing a winning ticket
- the winning ticket awarding a larger prize.
This is computed by multiplying the probabilities of the two independent events:
[tex]\[
\text{Probability of larger prize ticket} = \left( \frac{3}{5} \right) \times \left( \frac{1}{3} \right) = \frac{3 \times 1}{5 \times 3} = \frac{3}{15} = \frac{1}{5}
\][/tex]
Therefore, the probability that a randomly chosen ticket will award a larger prize is:
[tex]\[
\boxed{\frac{1}{5}}
\][/tex]
