To determine the probability that a randomly chosen ticket will award a larger prize, let's break down the problem into manageable parts using the given information.
1. Determine the probability of selecting a winning ticket:
We are given that six out of every 10 tickets are winning tickets. Therefore, the probability of selecting a winning ticket (P(W)) is:
[tex]\[
P(\text{Winning}) = \frac{6}{10} = 0.6
\][/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. Hence, the probability of getting a larger prize given that we have a winning ticket (P(Large | Winning)) is:
[tex]\[
P(\text{Large} | \text{Winning}) = \frac{1}{3} \approx 0.333
\][/tex]
3. Calculate the probability of getting a larger prize:
The overall probability that a ticket awards a larger prize (P(Large)) is found by multiplying the probability of selecting a winning ticket by the probability that a winning ticket awards a larger prize:
[tex]\[
P(\text{Large}) = P(\text{Winning}) \times P(\text{Large} | \text{Winning}) = 0.6 \times 0.333 = 0.2
\][/tex]
4. Convert the probability to a fraction:
To match the answer to given options, we express this probability in fraction form. We know:
[tex]\[
0.2 = \frac{1}{5}
\][/tex]
Therefore, the probability that a randomly chosen ticket will award a larger prize is:
[tex]\[
\boxed{\frac{1}{5}}
\][/tex]
