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: Calculate probability of winning ticket

The probability of getting a winning - ticket is the ratio of winning tickets to total tickets. Given 6 out of 10 tickets are winning tickets, so the probability of getting a winning ticket $P(W)=\frac{6}{10}=\frac{3}{5}$.

Step2: Calculate probability of larger - prize among winning tickets

Given that 1 out of 3 winning tickets is a larger - prize, so the probability of getting a larger - prize among winning tickets $P(L|W)=\frac{1}{3}$.

Step3: Use the multiplication rule of probability

The multiplication rule for conditional probability is $P(L)=P(W)\times P(L|W)$. Substitute $P(W)=\frac{3}{5}$ and $P(L|W)=\frac{1}{3}$ into the formula: $P(L)=\frac{3}{5}\times\frac{1}{3}=\frac{3\times1}{5\times3}=\frac{1}{5}$.

Answer:

B. $\frac{1}{5}$