Discover the best answers to your questions with the help of IDNLearn.com. Find accurate and detailed answers to your questions from our experienced and dedicated community members.
Sagot :
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]
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]
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Your questions deserve reliable answers. Thanks for visiting IDNLearn.com, and see you again soon for more helpful information.