To solve the problem of finding the probability that a randomly chosen ticket will award a larger prize, we need to follow a step-by-step approach.
1. Determine the probability of picking a winning ticket:
According to the problem, six out of every ten tickets are winning tickets. Therefore, the probability of picking a winning ticket is:
[tex]\[
\frac{6}{10} = \frac{3}{5}
\][/tex]
2. Determine the probability that a winning ticket awards a larger prize:
Of the winning tickets, one out of every three awards a larger prize. Therefore, the probability that a winning ticket awards a larger prize is:
[tex]\[
\frac{1}{3}
\][/tex]
3. Calculate the total probability that a randomly chosen ticket awards a larger prize:
We need to find the combined probability that a randomly chosen ticket is a winning ticket and that it awards a larger prize. This involves multiplying the two probabilities found in the previous steps:
[tex]\[
\text{Probability of a larger prize} = \left( \frac{3}{5} \right) \times \left( \frac{1}{3} \right)
\][/tex]
4. Perform the multiplication:
[tex]\[
\left( \frac{3}{5} \right) \times \left( \frac{1}{3} \right) = \frac{3 \times 1}{5 \times 3} = \frac{3}{15} = \frac{1}{5}
\][/tex]
Therefore, the probability that a ticket randomly chosen will award a larger prize is:
[tex]\[
\boxed{\frac{1}{5}}
\][/tex]
So, the correct answer is:
[tex]\[
\frac{1}{5}
\][/tex]
