in the drawing, six out of every 10 tickets are winning tickets. of the winning tickets, one out of every…

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?\n$\frac{2}{15}$\n$\frac{1}{5}$\n$\frac{5}{9}$\n$\frac{5}{6}$

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?\n$\frac{2}{15}$\n$\frac{1}{5}$\n$\frac{5}{9}$\n$\frac{5}{6}$

Answer

Explanation:

Step1: Find probability of winning ticket

The probability of getting a winning ticket is $\frac{6}{10}=\frac{3}{5}$ since 6 out of 10 tickets are winning.

Step2: Find probability of larger - prize among winning tickets

The probability of getting a larger - prize among the winning tickets is $\frac{1}{3}$.

Step3: Use multiplication rule for probability

The probability of getting a ticket that awards a larger prize is the product of the probability of getting a winning ticket and the probability of getting a larger - prize among the winning tickets. So $P=\frac{3}{5}\times\frac{1}{3}$. $P = \frac{3\times1}{5\times3}=\frac{1}{5}$

Answer:

$\frac{1}{5}$