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In the drawing, six out of every ten tickets are winning tickets. Of the winning tickets, one out of every three awards a larger prize.

What is the probability that a ticket that is randomly chosen will award a larger prize?

A. [tex]$\frac{2}{15}$[/tex]
B. [tex]$\frac{1}{5}$[/tex]
C. [tex]$\frac{5}{9}$[/tex]
D. [tex]$\frac{5}{6}$[/tex]


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]
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