Question

in the drawing, six out of every 10 tickets are winning tickets. of the winning tickets, one out of every three awards is a larger prize. what is the probability that a ticket that is randomly chosen will award a larger prize? \\(\frac{2}{15}\\) \\(\frac{1}{5}\\) \\(\frac{5}{9}\\) \\(\frac{5}{6}\\)

Explanation:

Step1: Find probability of winning ticket

Probability of winning ticket is $\frac{6}{10}=\frac{3}{5}$.

Step2: Find probability of larger prize given winning

Probability of larger prize given winning is $\frac{1}{3}$.

Step3: Multiply the two probabilities

To find the probability of a ticket awarding a larger prize, multiply the two probabilities: $\frac{3}{5} \times \frac{1}{3} = \frac{1}{5}$.

Answer:

$\frac{1}{5}$ (corresponding to the option with $\frac{1}{5}$)